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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 [1]. 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.

  • 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.

Return type:

NetworkX graph


>>> 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.


[1]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.