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overlap_weighted_projected_graph(B, nodes, jaccard=True)

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 :

$$w_{v, u} = \frac{|N(u) \cap N(v)|}{|N(u) \cup N(v)|}$$

or if the parameter 'jaccard' is False, the fraction of common neighbors by minimum of both nodes degree in the original bipartite graph :

$$w_{v, u} = \frac{|N(u) \cap N(v)|}{min(|N(u)|, |N(v)|)}$$

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.

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 <networkx.algorithms.bipartite> for further details on how bipartite graphs are handled in NetworkX.

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.

Overlap weighted projection of B onto one of its node sets.

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})]

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.bipartite.projection.collaboration_weighted_projected_graph networkx.algorithms.bipartite.projection.weighted_projected_graph networkx.algorithms.bipartite.projection.projected_graph networkx.algorithms.bipartite.projection.generic_weighted_projected_graph

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them