within_inter_cluster#
- within_inter_cluster(G, ebunch=None, delta=0.001, community='community')[source]#
Compute the ratio of within- and inter-cluster common neighbors of all node pairs in ebunch.
For two nodes
u
andv
, if a common neighborw
belongs to the same community as them,w
is considered as within-cluster common neighbor ofu
andv
. Otherwise, it is considered as inter-cluster common neighbor ofu
andv
. 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 nonexistent 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.
- Raises:
- NetworkXNotImplemented
If
G
is aDiGraph
, aMultigraph
or aMultiDiGraph
.- NetworkXAlgorithmError
If
delta
is less than or equal to zero.If no community information is available for a node in
ebunch
or inG
(ifebunch
isNone
).
- NodeNotFound
If
ebunch
has a node that is not inG
.
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