# 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