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overlap_weighted_projected_graph¶
- overlap_weighted_projected_graph(B, nodes, jaccard=True)[source]¶
Overlap weighted projection of B onto one of its node sets.
The overlap weighted projection is the projection of the bipartite network B onto the specified nodes with weights representing the Jaccard index between the neighborhoods of the two nodes in the original bipartite network [R162]:
\[w_{v,u} = \frac{|N(u) \cap N(v)|}{|N(u) \cup N(v)|}\]or if the parameter ‘jaccard’ is False, the fraction of common neighbors by minimum of both nodes degree in the original bipartite graph [R162]:
\[w_{v,u} = \frac{|N(u) \cap N(v)|}{min(|N(u)|,|N(v)|)}\]The nodes retain their attributes and are connected in the resulting graph if have an edge to a common node in the original bipartite graph.
Parameters : B : NetworkX graph
The input graph should be bipartite.
nodes : list or iterable
Nodes to project onto (the “bottom” nodes).
jaccard: Bool (default=True)
Returns : Graph : NetworkX graph
A graph that is the projection onto the given nodes.
See also
is_bipartite, is_bipartite_node_set, sets, weighted_projected_graph, collaboration_weighted_projected_graph, generic_weighted_projected_graph, projected_graph
Notes
No attempt is made to verify that the input graph B is bipartite. The graph and node properties are (shallow) copied to the projected graph.
References
[R162] (1, 2, 3) Borgatti, S.P. and Halgin, D. In press. Analyzing Affiliation Networks. In Carrington, P. and Scott, J. (eds) The Sage Handbook of Social Network Analysis. Sage Publications. Examples
>>> from networkx.algorithms import bipartite >>> B = nx.path_graph(5) >>> G = bipartite.overlap_weighted_projected_graph(B, [0, 2, 4]) >>> print(G.nodes()) [0, 2, 4] >>> print(G.edges(data=True)) [(0, 2, {'weight': 0.5}), (2, 4, {'weight': 0.5})] >>> G = bipartite.overlap_weighted_projected_graph(B, [0, 2, 4], jaccard=False) >>> print(G.edges(data=True)) [(0, 2, {'weight': 1.0}), (2, 4, {'weight': 1.0})]