updates

xgi/generators/uniform.py

@@ -347,13 +347,17 @@ def uniform_erdos_renyi_hypergraph(n, m, p, p_type="prob", multiedges=False, see
 
     Notes
     -----
-    Because XGI only stores edges as sets, if self-loops are allowed,
-    for example, the edge (0, 0, 0) will be mapped to {0}. However,
-    because this is explicitly a *uniform* method, we discard these edges. 
-    For sparse networks, this is a rare
-    occurrence and this method offers an order of magnitude speedup,
-    so while it is not the default behavior, this option is exposed to
-    the users by setting `multiedges=True`.
+    When `multiedges=True`, there is the possibility of generating
+    (potentially unwanted) artifacts, like multiedges and loopy
+    hyperedges which are not present in the original Erdos-Renyi model.
+    Because hypergraphs in XGI only store edges as sets, when an edge
+    such as (0, 0, 0) is generated will be mapped to {0}. However,
+    because this is explicitly a *uniform* method, we discard these edges.
+    For sparse networks, this is a rare occurrence and allowing these
+    artifacts offers an order of magnitude speedup. Although allowing
+    loopy hyperedges and multiedges is not the default behavior, this
+    (as well as the associated performance boost) is enabled by setting
+    `multiedges=True`.
 
     References
     ----------
@@ -408,6 +412,9 @@ def uniform_erdos_renyi_hypergraph(n, m, p, p_type="prob", multiedges=False, see
         # will not longer be uniform, so we discard them.
         if len(e) == m:
             H.add_edge(e)
+        # We no longer subtract 1 because if we did, the minimum
+        # value of the right-hand side would be zero, meaning that
+        # we sample the same index multiple times.
         index += np.random.geometric(q)
     return H
 
@@ -416,6 +423,8 @@ def _index_to_edge_prod(index, n, m):
     """Generate a hyperedge from an index given the
     number of nodes and size of hyperedges.
 
+    In this method, it treats each edge permutation as distinct, which can
+    lead to multiedges and loopy edges, especially for dense hypergraphs.
     Imagine that there is a hypergraph with 4 nodes and an edge size of 3.
     We write out each edge (allowing duplicate entries) incrementing the last entry first,
     followed by the second-to-last entry and so on, with each edge corresponding to an index
@@ -424,15 +433,11 @@ def _index_to_edge_prod(index, n, m):
     This function will, for instance,
     return (0, 0, 3) for index 3, network size 4, and edge size 3.
 
-    Because XGI only stores edges as sets, the edge (0, 0, 0) will be mapped
-    to {0}. However, because this is explicitly a *uniform* method, we discard
-    these edges so that this is the case. For sparse networks, this is a rare
-    occurrence and this method offers an order of magnitude speedup, so while
-    it is not the default behavior.
-
-    This method treats each edge permutation as distinct, which can
-    lead to multiedges, especially for dense hypergraphs.
-
+    Because hypergraphs in XGI only store edges as sets, the edge (0, 0, 0),
+    for example, generated by this function will be mapped to {0}. However,
+    because this is explicitly a *uniform* method, we discard these edges.
+    For sparse networks, this is a rare occurrence and this method offers
+    an order of magnitude speedup.
 
     Parameters
     ----------
@@ -471,8 +476,8 @@ def _index_to_edge_comb(index, n, m):
     return (0, 2, 3) for index 2, network size 4, and edge size 3.
 
 
-    In this function, we prohibit multiedges, so each index corresponds to a
-    unique edge.
+    In this function, we prohibit multiedges, so each edge corresponds to a
+    unique index.
 
     Parameters
     ----------