networkx.algorithms.link_prediction.adamic_adar_index

adamic_adar_index(G, ebunch=None)

Compute the Adamic-Adar index of all node pairs in ebunch.

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

• G (graph) – NetworkX undirected graph.

• ebunch (iterable 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

piter – 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.

Return type

iterator

Examples

>>> G = nx.complete_graph(5)
>>> preds = nx.adamic_adar_index(G, [(0, 1), (2, 3)])
>>> for u, v, p in preds:
...     print(f"({u}, {v}) -> {p:.8f}")
(0, 1) -> 2.16404256
(2, 3) -> 2.16404256

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