Data Science/Graph-Mining-with-Networkx/7-embedding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SD212: Graph mining\n",
    "## Lab 7: Graph embedding\n",
    "\n",
    "You will learn how to embed the nodes of a graph in some low-dimensional space using the spectral decomposition of the Laplacian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.sparse as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hint:** To get the documentation on a `function` you can type `function?`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.to_scipy_sparse_matrix?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "You will need the following datasets (the same as in previous labs, no need to download them again):\n",
    "* [Les Misérables](http://perso.telecom-paristech.fr/~bonald/graphs/miserables.graphml.gz)<br>  Graph connecting the characters of the [novel of Victor Hugo](https://fr.wikisource.org/wiki/Les_Misérables) when they appear in the same chapter. The graph is undirected and weighted. Weights correspond to the number of chapters in which characters appear together. \n",
    "* [Openflights](http://perso.telecom-paristech.fr/~bonald/graphs/openflights.graphml.gz)<br>\n",
    "Graph of the main international flights. Nodes are airports. The graph is undirected (all flights are bidirectional). Weights correspond to the number of daily flights between airports. Extracted from [Openflights](http://openflights.org).\n",
    "* [Wikipedia for schools](http://perso.telecom-paristech.fr/~bonald/graphs/wikipedia_schools.graphml.gz)<br> Graph of the hyperlinks between a subset of the pages of the English Wikipedia. The graph is directed and unweighted.\n",
    "More information [here](https://en.wikipedia.org/wiki/Wikipedia:Wikipedia_for_Schools)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Random walk\n",
    "\n",
    "Consider an undirected graph of $n$ nodes with adjacency matrix $A$. \n",
    "Let $D = \\text{diag}(w)$ be the diagonal matrix of node weights, with $w = A1$.\n",
    "The transition matrix of the random walk is defined by $P = D^{-1}A$. This is a stochastic matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Toy graph\n",
    "\n",
    "Consider the following graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "window.mpl = {};\n",
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       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
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       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
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       "\n",
       "    this.imageObj = new Image();\n",
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       "    this.canvas = undefined;\n",
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       "\n",
       "    $(parent_element).append(this.root);\n",
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       "            fig.send_message(\"send_image_mode\", {});\n",
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       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
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       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
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       "            pass_mouse_events = false;\n",
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       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
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       "\n",
       "    function mouse_event_fn(event) {\n",
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       "            return fig.mouse_event(event, event['data']);\n",
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       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
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       "\n",
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       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
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       "        return false;\n",
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       "\n",
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       "        canvas_div.focus();\n",
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       "\n",
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       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
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       "        return fig.toolbar_button_onclick(event['data']);\n",
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       "    function toolbar_mouse_event(event) {\n",
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       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = nx.lollipop_graph(3, 5)\n",
    "nx.draw(graph, with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "adjacency = nx.to_scipy_sparse_matrix(graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def transition_matrix(adjacency):\n",
    "    n = adjacency.shape[0]\n",
    "    weights = adjacency.dot(np.ones(n))\n",
    "    inverse_weight_matrix = sp.diags(1 / weights, format='csr')\n",
    "    return inverse_weight_matrix.dot(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = transition_matrix(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = adjacency.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Stochastic matrix\n",
    "P.dot(np.ones(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To do\n",
    "\n",
    "* Complete the function `random_walk` below that compute the distribution of the random walk after `N` steps.\n",
    "* Check the convergence to the stationary distribution on the above toy graph (e.g., starting from the uniform distribution)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_walk(adjacency, start, N = 10):\n",
    "    '''\n",
    "    adjacency: scipy CSR matrix\n",
    "        adjacency matrix\n",
    "    start: np array\n",
    "        initial distribution (sums to 1)\n",
    "    N: int\n",
    "        number of steps\n",
    "        \n",
    "    Returns: np array\n",
    "        distribution after N steps\n",
    "    '''    \n",
    "    distribution = start\n",
    "    for i in range(N):\n",
    "        distribution = transition_matrix(adjacency).dot(distribution)\n",
    "    # to be completed\n",
    "    return distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.125,  0.125,  0.125,  0.125,  0.125,  0.125,  0.125,  0.125])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init = 1/8*np.ones(8)\n",
    "random_walk(adjacency,init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Laplacian\n",
    "\n",
    "The Laplacian matrix is defined by:\n",
    "$$\n",
    "L = D - A.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def laplacian_matrix(adjacency):\n",
    "    n = adjacency.shape[0]\n",
    "    weights = adjacency.dot(np.ones(n))\n",
    "    weight_matrix = sp.diags(weights, format='csr')\n",
    "    return weight_matrix - adjacency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = laplacian_matrix(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = adjacency.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.dot(np.ones(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heat equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Laplacian is related to a diffusion process on the graph governed by the heat equation,\n",
    "$$\n",
    "\\forall i\\not \\in S, \\quad  \\frac{dT_i}{dt} = -(LT)_i,\n",
    "$$\n",
    "where $T_i$ be the temperature of node $i$ and $S$ the boundary where temperature is fixed. \n",
    "\n",
    "The solution satisfies:\n",
    "$$\n",
    "\\forall i\\not \\in S, \\quad(LT)_i = 0,\n",
    "$$\n",
    "or equivalently,\n",
    "$$\n",
    "\\forall i\\not \\in S, \\quad T_i = (PT)_i.\n",
    "$$\n",
    "\n",
    "This is the [Dirichlet problem](https://en.wikipedia.org/wiki/Dirichlet_problem).\n",
    "The easiest way to compute the solution to the Dirichlet problem is to use the diffusion in discrete time:\n",
    "$$\n",
    "\\forall i\\not \\in S, \\quad T_i \\gets (PT)_i.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To do\n",
    "\n",
    "* Complete the `diffusion` function below that returns the temperature of each node after $N$ iterations of the  diffusion in discrete time, when the boundary set $S$ consists of two sets of nodes: the `sources` at temperature 0 and the `targets` at temperature 1. \n",
    "* Show the heat map of the above toy graph, for one source and one target of your choice. You may print the vector $LT$.\n",
    "* Show the heat map of Les Miserables after the diffusion from Cosette and Fantine (sources) to Marius (target). What is the hotest node after Marius?\n",
    "* Show the heat map of Openflights after the diffusion from Charles-de-Gaulle Airport (source) to Beijing Capital International Airport (target). \n",
    "* Display the 5 hotest pages of Wikipedia for Schools (considered as undirected) after diffusion from Cat to Dog. Compare with the 5 top-pages for the  Personalized PageRank associated to Dog."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffusion(adjacency, sources, targets, N = 100):\n",
    "    '''\n",
    "    adjacency: scipy CSR matrix\n",
    "        adjacency matrix\n",
    "    sources: list of int\n",
    "        nodes at temperature 0\n",
    "    targets: list of int\n",
    "        nodes at temperature 1\n",
    "    N: int\n",
    "        number of steps\n",
    "        \n",
    "    Returns: np array\n",
    "        temperature after N steps\n",
    "    '''    \n",
    "    n = adjacency.shape[0]\n",
    "    T = 0.5 * np.ones(n, float)\n",
    "    sources = np.array(sources)\n",
    "    targets = np.array(targets)\n",
    "    T[sources] = 0\n",
    "    T[targets] = 1\n",
    "    L = laplacian_matrix(adjacency)\n",
    "    P = transition_matrix(adjacency)\n",
    "    for t in range(N):\n",
    "        new_T=P.dot(T)\n",
    "        for i in range(n):\n",
    "            if i not in sources and i not in targets:\n",
    "                T[i]=new_T[i]\n",
    "    return T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = adjacency.shape[0]\n",
    "T = diffusion(adjacency, [0], [n-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "nx.draw(graph, with_labels = True, node_color = T, cmap = 'coolwarm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "miserables = nx.read_graphml(\"miserables.graphml\", node_type = int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "name = nx.get_node_attributes(miserables, 'name')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "cosette = 26 #source\n",
    "fantine = 23 #source\n",
    "marius = 55 #target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "adjacency  = nx.to_numpy_array(miserables)\n",
    "n = adjacency.shape[0]\n",
    "T = diffusion(adjacency, [cosette,fantine], [marius])\n",
    "plt.figure()\n",
    "nx.draw(miserables, with_labels = True, node_color = T, cmap = 'coolwarm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "openflights = nx.read_graphml(\"openflights.graphml\", node_type = int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get positions\n",
    "pos_x = nx.get_node_attributes(openflights,'pos_x')\n",
    "pos_y = nx.get_node_attributes(openflights,'pos_y')\n",
    "pos = {u: (pos_x[u], pos_y[u]) for u in openflights.nodes()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "name = nx.get_node_attributes(openflights, 'name')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "cdg = 622\n",
    "beijing = 1618"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id='26742f66-0561-49b6-a99b-bc5d520c7647'></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "adjacency  = nx.to_numpy_array(openflights)\n",
    "n = adjacency.shape[0]\n",
    "T = diffusion(adjacency, [cdg], [beijing])\n",
    "plt.figure()\n",
    "nx.draw(openflights, with_labels = True, node_color = T, cmap = 'coolwarm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wikipedia = nx.read_graphml(\"wikipedia_schools.graphml\", node_type = int).to_undirected()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "name = nx.get_node_attributes(wikipedia, 'name')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dog = 1408\n",
    "cat = 2515"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "adjacency  = nx.to_numpy_array(wikipedia)\n",
    "n = adjacency.shape[0]\n",
    "T = diffusion(adjacency, [cdg], [beijing])\n",
    "plt.figure()\n",
    "nx.draw(wikipedia, with_labels = True, node_color = T, cmap = 'coolwarm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Spectral embedding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $v_1,\\ldots,v_n$ be the eigenvectors of the Laplacian matrix, with corresponding eigenvalues $\\lambda_1= 0 < \\lambda_2 \\le  \\ldots \\le \\lambda_{n}$. The spectral embedding of the graph in dimension $k$ is given by the following $n\\times k$ matrix:\n",
    "$$\n",
    "X = \\left(\\frac {v_2} {\\sqrt{\\lambda_2}},\\ldots,\\frac {v_{k+1}} {\\sqrt{\\lambda_{k+1}}}\\right)^T.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def spectral_decomposition_laplacian(adjacency, number = None):\n",
    "    '''\n",
    "    adjacency: scipy CSR matrix\n",
    "        adjacency matrix\n",
    "    number: int\n",
    "        number of eigenvalues / eigenvectors\n",
    "        \n",
    "    Returns: (np array, np.array)\n",
    "        eigenvalues, eigenvectors of the Laplacian matrix\n",
    "    '''    \n",
    "    n = adjacency.shape[0]\n",
    "    if number == None or number >= n: # full spectrum\n",
    "        number = n - 1\n",
    "    laplacian = laplacian_matrix(adjacency)\n",
    "    eigenvalues, eigenvectors = sp.linalg.eigsh(laplacian, number, sigma = -1)\n",
    "    index = np.argsort(eigenvalues)\n",
    "    eigenvalues = eigenvalues[index]\n",
    "    eigenvectors = eigenvectors[:,index]\n",
    "    return eigenvalues, eigenvectors "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To do \n",
    "\n",
    "* Plot the spectrum of the Laplacian matrix associated with the toy graph, as well as the heat map of the graph associated with the Fiedler vector $v_2$\n",
    "* Complete the function `spectral_embedding` below that returns the spectral embedding $X$\n",
    "* Display the 2D embedding of the toy graph\n",
    "* Display the 2D embedding of Les Miserables (with names)\n",
    "* List the 5 closest nodes from Marius in terms of cosine similarity in the embedding of Les Miserables in dimension 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Spectrum of the laplacian matrix associated to the toy graph\n",
    "\n",
    "L = laplacian_matrix(adjacency)\n",
    "eigenvalues, eigenvectors = sp.linalg.eigsh(L, n-1, sigma = -1)\n",
    "index = np.argsort(eigenvalues)\n",
    "eigenvalues = eigenvalues[index]\n",
    "eigenvectors = eigenvectors[:,index]\n",
    "print(eigenvalues)\n",
    "print(eigenvectors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def spectral_embedding(adjacency, k = 10):\n",
    "    '''\n",
    "    adjacency: scipy CSR matrix\n",
    "        adjacency matrix\n",
    "    k: int\n",
    "        dimension of the embedding\n",
    "        \n",
    "    Returns: np array\n",
    "        spectral embedding (based on the Laplacian)\n",
    "    '''    \n",
    "    n = adjacency.shape[0]\n",
    "    # to be completed\n",
    "    if k == None or k >= n-1: # full dimension\n",
    "        k = n - 2\n",
    "    \n",
    "    X = np.zeros((n,k))\n",
    "    \n",
    "    eival, eivec = spectral_decomposition_laplacian(adjacency,k+1)\n",
    "    \n",
    "    for p in tqdm(range(k)):\n",
    "        X[:,p] = eivec[:,p+1] * (1/eival[p+1])\n",
    "    \n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = spectral_embedding(adjacency, k = 2)\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Display the 2D embedding of the toy graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "nx.draw(graph, pos=X, with_labels=True, node_color = T, cmap = 'coolwarm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cosine_similarity(X, node):\n",
    "    '''\n",
    "    X: np array\n",
    "        embedding\n",
    "    node: int\n",
    "        target node\n",
    "        \n",
    "    Returns: np array\n",
    "        cosine similarity with all other nodes\n",
    "    '''        \n",
    "    cosine = X.dot(X[node,:]) / np.linalg.norm(X, axis = 1) / np.linalg.norm(X[node,:])\n",
    "    return cosine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Display the 2D embedding of Les Miserables (with names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "XM = spectral_embedding(adjacencyM, k = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "nx.draw(miserables, pos=XM, with_labels=True, node_color = TM, cmap = 'coolwarm', labels=nameM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def closest_cosine(X,node,N=5,names=nameM):\n",
    "    n=X.shape[0]\n",
    "    x = X[node,:]\n",
    "    d = np.array(list(np.linalg.norm(x - X[i,:]) for i in range(n)))\n",
    "    closest = []\n",
    "    for k in range(N+1):\n",
    "        imin = np.argmin(d)\n",
    "        #print(d[imin])\n",
    "        if d[imin] > 0:\n",
    "            closest.append(imin)\n",
    "        d[imin] = 1e500\n",
    "    return [names[i] for i in closest]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "closest_cosine(XM10,marius)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To do\n",
    "\n",
    "* Plot the 10 first eigenvalues of the Laplacian associated with Wikipedia for Schools. What do you observe?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wiki_eival, wiki_eivec = spectral_decomposition_laplacian(adjacencyW,11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.scatter(range(wiki_eival.shape[0]),wiki_eival)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* List the 10 closest nodes from Dog in terms of cosine similarity in the embedding of Wikipedia for Schools in dimension 50. Redo the experiment after removing the first component of the embedding. Interpret the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "XW50 = spectral_embedding(adjacencyW, k = 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "closest_cosine(XW50,dog,names=nameW)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "closest_cosine(XW50[1:,],dog,names=nameW)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another spectral embedding is based on the spectral decomposition of the transition matrix. This amounts to weight each node by its weight in the graph. Let $v_1,\\ldots,v_n$ be the eigenvectors of $P$, with corresponding eigenvalues $\\lambda_1= 1 > \\lambda_2 \\ge  \\ldots \\ge \\lambda_{n}$. The weighted spectral embedding of the graph in dimension $k$ is given by the following $n\\times k$ matrix:\n",
    "$$\n",
    "Y = \\left(\\frac {v_2} {\\sqrt{1-\\lambda_2}},\\ldots,\\frac {v_{k+1}} {\\sqrt{1-\\lambda_{k+1}}}\\right)^T.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To do\n",
    "\n",
    "* Complete the functions `spectral_decomposition_transition` and `weighted_spectral_embedding` below. <br>\n",
    "**Note:** The spectral decomposition of the transition matrix involves the normalized adjacency matrix $D^{-1/2}AD^{-1/2}$ (cf. Theorem 1 in the lecture notes).\n",
    "* Do the same experiments as above for this new embedding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def spectral_decomposition_transition(adjacency, number = None):\n",
    "    '''\n",
    "    adjacency: scipy CSR matrix\n",
    "        adjacency matrix\n",
    "    number: int\n",
    "        number of eigenvalues / eigenvectors\n",
    "        \n",
    "    Returns: (np array, np.array)\n",
    "        eigenvalues, eigenvectors of the transition matrix\n",
    "    '''    \n",
    "    n = adjacency.shape[0]\n",
    "    if (number != None):\n",
    "        k = min(number,n-1)\n",
    "    else:\n",
    "        k = n-1\n",
    "    eigenvalues = np.zeros(k)\n",
    "    eigenvectors = np.zeros((n,k))\n",
    "    # to be completed\n",
    "    W = adjacency.dot(np.ones(n))\n",
    "    D = np.diag(W)\n",
    "    Dsqu = np.linalg.inv(scipy.linalg.sqrtm(D))\n",
    "    norm_adjacency = Dsqu.dot(adjacency.dot(Dsqu))\n",
    "    eigenvalues, eigenvectors = sp.linalg.eigsh(norm_adjacency, k, which='LA')\n",
    "    return eigenvalues, eigenvectors "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def weighted_spectral_embedding(adjacency, k = 10):\n",
    "    '''\n",
    "    adjacency: scipy CSR matrix\n",
    "        adjacency matrix\n",
    "    k: int\n",
    "        dimension of the embedding\n",
    "        \n",
    "    Returns: np array\n",
    "        weighted spectral embedding (based on the transition matrix)\n",
    "    '''\n",
    "    n = adjacency.shape[0]\n",
    "    if k > n-1:\n",
    "        k = n-1\n",
    "    Y = np.zeros((n,k))\n",
    "    eival, eivec = spectral_decomposition_transition(adjacency)\n",
    "    for p in tqdm(range(k)):\n",
    "        Y[:,p] = eivec[:,p+1] * 1/(1 - eival[p+1])\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_weighted = weighted_spectral_embedding(adjacency, k = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "XM10_weighted = weighted_spectral_embedding(adjacencyM, k = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "closest_cosine(XM10_weighted,marius)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "closest_cosine(XM10_weighted[1:,],marius)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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