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 [1]:
\[w_{v, u} = \frac{|N(u) \cap N(v)|}{|N(u) \cup N(v)|}\]or if the parameter âjaccardâ is False, the fraction of common neighbors by minimum of both nodes degree in the original bipartite graph [1]:
\[w_{v, u} = \frac{|N(u) \cap N(v)|}{min(|N(u)|, |N(v)|)}\]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:
- BNetworkX graph
The input graph should be bipartite.
- nodeslist or iterable
Nodes to project onto (the âbottomâ nodes).
- jaccard: Bool (default=True)
- Returns:
- GraphNetworkX 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.
See
bipartite documentation
for further details on how bipartite graphs are handled in NetworkX.References
Examples
>>> from networkx.algorithms import bipartite >>> B = nx.path_graph(5) >>> nodes = [0, 2, 4] >>> G = bipartite.overlap_weighted_projected_graph(B, nodes) >>> list(G) [0, 2, 4] >>> list(G.edges(data=True)) [(0, 2, {'weight': 0.5}), (2, 4, {'weight': 0.5})] >>> G = bipartite.overlap_weighted_projected_graph(B, nodes, jaccard=False) >>> list(G.edges(data=True)) [(0, 2, {'weight': 1.0}), (2, 4, {'weight': 1.0})]