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# weighted_projected_graph¶

weighted_projected_graph(B, nodes, ratio=False)[source]

Returns a weighted projection of B onto one of its node sets.

The weighted projected graph is the projection of the bipartite network B onto the specified nodes with weights representing the number of shared neighbors or the ratio between actual shared neighbors and possible shared neighbors if ratio=True . The nodes retain their attributes and are connected in the resulting graph if they have an edge to a common node in the original graph.

Parameters: B (NetworkX graph) – The input graph should be bipartite. nodes (list or iterable) – Nodes to project onto (the “bottom” nodes). ratio (Bool (default=False)) – If True, edge weight is the ratio between actual shared neighbors and possible shared neighbors. If False, edges weight is the number of shared neighbors. Graph – A graph that is the projection onto the given nodes. NetworkX graph

Examples

>>> from networkx.algorithms import bipartite
>>> B = nx.path_graph(4)
>>> G = bipartite.weighted_projected_graph(B, [1,3])
>>> print(G.nodes())
[1, 3]
>>> print(G.edges(data=True))
[(1, 3, {'weight': 1})]
>>> G = bipartite.weighted_projected_graph(B, [1,3], ratio=True)
>>> print(G.edges(data=True))
[(1, 3, {'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.

References

  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.