jaccard_coefficient#

Compute the Jaccard coefficient of all node pairs in ebunch.

Jaccard coefficient of nodes u and v is defined as

\[\frac{|\Gamma(u) \cap \Gamma(v)|}{|\Gamma(u) \cup \Gamma(v)|}\]

where \(\Gamma(u)\) denotes the set of neighbors of \(u\).

Parameters:
Ggraph

A NetworkX undirected graph.

ebunchiterable of node pairs, optional (default = None)

Jaccard coefficient will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all nonexistent edges in the graph will be used. Default value: None.

Returns:
piteriterator

An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their Jaccard coefficient.

Raises:
NetworkXNotImplemented

If G is a DiGraph, a Multigraph or a MultiDiGraph.

NodeNotFound

If ebunch has a node that is not in G.

References

[1]

D. Liben-Nowell, J. Kleinberg. The Link Prediction Problem for Social Networks (2004). http://www.cs.cornell.edu/home/kleinber/link-pred.pdf

Examples

>>> G = nx.complete_graph(5)
>>> preds = nx.jaccard_coefficient(G, [(0, 1), (2, 3)])
>>> for u, v, p in preds:
...     print(f"({u}, {v}) -> {p:.8f}")
(0, 1) -> 0.60000000
(2, 3) -> 0.60000000

Additional backends implement this function

cugraph : GPU-accelerated backend.

neptuneNeptune computation backend for NetworkX.

  • The ebunch parameter must be provided as an iterable of node pairs (u, v).

  • When ebunch=None, non-edges are computed locally from the NetworkX graph before being sent to Neptune. For large graphs, prefer passing an explicit ebunch.

  • Neptune Analytics does not support a mutate variant for Jaccard similarity.

  • For additional parameters, see awslabs/nx-neptune

parallelA networkx backend that uses joblib to run graph algorithms in parallel. Find the nx-parallel’s configuration guide here

The edge pairs are chunked into pairs_chunks and then the jaccard coefficient for all pairs_chunks is computed in parallel over n_jobs number of CPU cores.

Additional parameters:
get_chunksstr, function (default = “chunks”)

A function that takes in a list of all the edges (or ebunch) as input and returns an iterable pairs_chunks. The default chunking is done by slicing ebunch into n_jobs number of chunks.

[Source]

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