within_inter_cluster¶

within_inter_cluster
(G, ebunch=None, delta=0.001, community='community')[source]¶ Compute the ratio of within and intercluster 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 withincluster common neighbor of \(u\) and \(v\). Otherwise, it is considered as intercluster common neighbor of \(u\) and \(v\). The ratio between the size of the set of within and intercluster common neighbors is defined as the WIC measure. [1]
Parameters:  G (graph) – A NetworkX undirected graph.
 ebunch (iterable 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 2tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all nonexistent edges in the graph will be used. Default value: None.
 delta (float, optional (default = 0.001)) – Value to prevent division by zero in case there is no intercluster common neighbor between two nodes. See [1] for details. Default value: 0.001.
 community (string, 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: piter – An iterator of 3tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their WIC measure.
Return type: iterator
Examples
>>> import networkx as nx >>> G = nx.Graph() >>> G.add_edges_from([(0, 1), (0, 2), (0, 3), (1, 4), (2, 4), (3, 4)]) >>> G.node[0]['community'] = 0 >>> G.node[1]['community'] = 1 >>> G.node[2]['community'] = 0 >>> G.node[3]['community'] = 0 >>> G.node[4]['community'] = 0 >>> preds = nx.within_inter_cluster(G, [(0, 4)]) >>> for u, v, p in preds: ... '(%d, %d) > %.8f' % (u, v, p) ... '(0, 4) > 1.99800200' >>> preds = nx.within_inter_cluster(G, [(0, 4)], delta=0.5) >>> for u, v, p in preds: ... '(%d, %d) > %.8f' % (u, v, p) ... '(0, 4) > 1.33333333'
References
[1] (1, 2) Jorge Carlos ValverdeRebaza 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) http://dx.doi.org/10.1007/9783642344596_10