preferential_attachment¶

preferential_attachment(G, ebunch=None)[source]¶

Compute the preferential attachment score of all node pairs in ebunch.

Preferential attachment score of \(u\) and \(v\) is defined as

\[|\Gamma(u)| |\Gamma(v)|\]

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

Parameters:	G : graph NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) Preferential attachment score 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 : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their preferential attachment score.

References

[R270]

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

Examples

>>> import networkx as nx
>>> G = nx.complete_graph(5)
>>> preds = nx.preferential_attachment(G, [(0, 1), (2, 3)])
>>> for u, v, p in preds:
...     '(%d, %d) -> %d' % (u, v, p)
...
'(0, 1) -> 16'
'(2, 3) -> 16'