# preferential_attachment#

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
Ggraph

NetworkX undirected graph.

ebunchiterable 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
piteriterator

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

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.preferential_attachment(G, [(0, 1), (2, 3)])
>>> for u, v, p in preds:
...     print(f"({u}, {v}) -> {p}")
(0, 1) -> 16
(2, 3) -> 16