Adamic-Adar index of u and v is defined as

$\sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{\log |\Gamma(w)|}$

where $$\Gamma(u)$$ denotes the set of neighbors of $$u$$. This index leads to zero-division for nodes only connected via self-loops. It is intended to be used when no self-loops are present.

Parameters:
Ggraph

NetworkX undirected graph.

ebunchiterable of node pairs, optional (default = None)

Adamic-Adar index 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 non-existent 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 Adamic-Adar index.

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)