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collaboration_weighted_projected_graph¶

collaboration_weighted_projected_graph
(B, nodes)[source]¶ Newman’s weighted projection of B onto one of its node sets.
The collaboration weighted projection is the projection of the bipartite network B onto the specified nodes with weights assigned using Newman’s collaboration model [1]:
where and are nodes from the same bipartite node set, and is a node of the opposite node set. The value is the degree of node in the bipartite network and is 1 if node is linked to node in the original bipartite graph or 0 otherwise.
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).
Returns: Graph – A graph that is the projection onto the given nodes.
Return type: NetworkX graph
Examples
>>> from networkx.algorithms import bipartite >>> B = nx.path_graph(5) >>> B.add_edge(1,5) >>> G = bipartite.collaboration_weighted_projected_graph(B, [0, 2, 4, 5]) >>> print(G.nodes()) [0, 2, 4, 5] >>> for edge in G.edges(data=True): print(edge) ... (0, 2, {'weight': 0.5}) (0, 5, {'weight': 0.5}) (2, 4, {'weight': 1.0}) (2, 5, {'weight': 0.5})
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.
See also
is_bipartite()
,is_bipartite_node_set()
,sets()
,weighted_projected_graph()
,overlap_weighted_projected_graph()
,generic_weighted_projected_graph()
,projected_graph()
References
[1] Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001).