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 [R124]:
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or if the parameter ‘jaccard’ is False, the fraction of common
neighbors by minimum of both nodes degree in the original
bipartite graph [R124]:
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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.
|
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
[R124] | (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})]