README.md

Grand Isomorphisms

Subgraph isomorphism is a resource-heavy (but branch-parallelizable) algorithm that is hugely impactful for large graph analysis. SotA algorithms for this (Ullmann, VF2, BB-Graph) are heavily RAM-bound, but this is due to a large number of small processes each of which hold a small portion of a traversal tree in memory.

Grand-Iso is a subgraph isomorphism algorithm that exchanges this resource-limitation for a parallelizable partial-match queue structure.

It performs favorably compared to other pure-python (and even some non-pure-python!) implementations:

Example Usage

from grandiso import find_motifs
import networkx as nx

host = nx.fast_gnp_random_graph(10, 0.5)

motif = nx.Graph()
motif.add_edge("A", "B")
motif.add_edge("B", "C")
motif.add_edge("C", "D")
motif.add_edge("D", "A")

len(find_motifs(motif, host))

Directed graph support:

from grandiso import find_motifs
import networkx as nx

host = nx.fast_gnp_random_graph(10, 0.5, directed=True)

motif = nx.DiGraph()
motif.add_edge("A", "B")
motif.add_edge("B", "C")
motif.add_edge("C", "D")
motif.add_edge("D", "A")

len(find_motifs(motif, host))

Counts-only

For very large graphs, you may use a good chunk of RAM not only on the queue of hypotheses, but also on the list of results. If all you care about is the NUMBER of results, you should pass count_only=True to the find_motifs function. This will dramatically reduce your RAM overhead on higher-count queries.

All Arguments to find_motifs

Argument	Type	Default	Description
motif	nx.Graph		The motif to search for. Either a nx.Graph or nx.DiGraph. You can also pass something networkx.Graph-flavored, like a grand.Graph.
host	nx.Graph		The "haystack" graph to search within. Either a nx.Graph or nx.DiGraph. You can also pass something networkx.Graph-flavored, like a grand.Graph.
interestingness	dict	None	A lookup dictionary that assigns a floating number between 0 and 1 to each node in the motif graph. Nodes with values closest to 1 will be preferred when the candidate-mapper advances the exploration front. If this doesn't make sense to you, you can ignore this argument entirely. If none is provided, this will default to a uniform interestness metric where all nodes are considered equally.
count_only	bool	False	Whether to return only a count of motifs, rather than a list of mappings. If you set this to True, you will get back an integer result, not a list of dicts.
directed	bool	None	Whether to enforce a directed/undirected search. True means enforce directivity; False means enforce undirected search. The default (None) will guess based upon your motif and host.
profile	bool	False	Whether to slow down execution but give you a better idea of where your RAM usage is going. This is better ignored unless you're debugging something particularly nuanced.
isomorphisms_only	bool	False	Whether to search only for isomorphisms. In other words, whether to search for edges that exist in the node-induced subgraph.

Pseudocode for "Grand-Iso" algorithm

- Accept a motif M, and a host graph H.
- Create an empty list for result storage, R.
- Create an empty queue, Q.
- Preprocessing
    - Identify the most "interesting" node in motif M, m1.
    - Add to Q a set of mappings with a single node, with one map for all
        nodes in H that satisfy the requirements of m1: degree, attributes, etc
- Motif Search
    - "Pop" a backbone B from Q
        - Identify as m1 the most interesting node in motif M that does not yet
            have a mapping assigned in B.
        - Identify all nodes that are valid mappings from the backbone to m1,
            based upon degree, attributes, etc.
        - If multiple nodes are valid candidates, add each new backbone to Q.
        - Otherwise, when all nodes in M have a valid mapping in B to H, add
            the mapping to the results set R.
    - Continue while there are still backbones in Q.
- Reporting
    - Return the set R to the user.

Hacking on this repo

Running Tests

coverage run --source=grandiso -m pytest

Citing

If this tool is helpful to your research, please consider citing it with:

# https://www.biorxiv.org/content/10.1101/2020.06.08.140533v1
@article{matelsky_2020_dotmotif,
    doi = {10.1101/2020.06.08.140533},
    url = {https://www.biorxiv.org/content/10.1101/2020.06.08.140533v1},
    year = 2020,
    month = {june},
    publisher = {BiorXiv},
    author = {Matelsky, Jordan K. and Reilly, Elizabeth P. and Johnson,Erik C. and Wester, Brock A. and Gray-Roncal, William},
    title = {{Connectome subgraph isomorphisms and graph queries with DotMotif}},
    journal = {BiorXiv}
}