within_inter_cluster#

Compute the ratio of within- and inter-cluster common neighbors of all node pairs in ebunch.

For two nodes u and v, if a common neighbor w belongs to the same community as them, w is considered as within-cluster common neighbor of u and v. Otherwise, it is considered as inter-cluster common neighbor of u and v. The ratio between the size of the set of within- and inter-cluster common neighbors is defined as the WIC measure. [1]

Parameters:
Ggraph

A NetworkX undirected graph.

ebunchiterable of node pairs, optional (default = None)

The WIC measure 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.

deltafloat, optional (default = 0.001)

Value to prevent division by zero in case there is no inter-cluster common neighbor between two nodes. See [1] for details. Default value: 0.001.

communitystring, optional (default = ‘community’)

Nodes attribute name containing the community information. G[u][community] identifies which community u belongs to. Each node belongs to at most one community. Default value: ‘community’.

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 WIC measure.

References

[1] (1,2)

Jorge Carlos Valverde-Rebaza and Alneu de Andrade Lopes. Link prediction in complex networks based on cluster information. In Proceedings of the 21st Brazilian conference on Advances in Artificial Intelligence (SBIA’12) https://doi.org/10.1007/978-3-642-34459-6_10

Examples

>>> G = nx.Graph()
>>> G.add_edges_from([(0, 1), (0, 2), (0, 3), (1, 4), (2, 4), (3, 4)])
>>> G.nodes[0]["community"] = 0
>>> G.nodes[1]["community"] = 1
>>> G.nodes[2]["community"] = 0
>>> G.nodes[3]["community"] = 0
>>> G.nodes[4]["community"] = 0
>>> preds = nx.within_inter_cluster(G, [(0, 4)])
>>> for u, v, p in preds:
...     print(f"({u}, {v}) -> {p:.8f}")
(0, 4) -> 1.99800200
>>> preds = nx.within_inter_cluster(G, [(0, 4)], delta=0.5)
>>> for u, v, p in preds:
...     print(f"({u}, {v}) -> {p:.8f}")
(0, 4) -> 1.33333333