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generic_weighted_projected_graph(B, nodes, weight_function=None)

The bipartite network B is projected on to the specified nodes with weights computed by a user-specified function. This function must accept as a parameter the neighborhood sets of two nodes and return an integer or a float.

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.

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).
weight_function : function: This function must accept as parameters the same input graph that this function, and two nodes; and return an integer or a float. The default function computes the number of shared neighbors.

Returns

Graph : NetworkX graph: A graph that is the projection onto the given nodes.

Weighted projection of B with a user-specified weight function.

Examples

>>> from networkx.algorithms import bipartite
... # Define some custom weight functions
... def jaccard(G, u, v):
...     unbrs = set(G[u])
...     vnbrs = set(G[v])
...     return float(len(unbrs & vnbrs)) / len(unbrs | vnbrs)
...

>>> def my_weight(G, u, v, weight="weight"):
...     w = 0
...     for nbr in set(G[u]) & set(G[v]):
...         w += G[u][nbr].get(weight, 1) + G[v][nbr].get(weight, 1)
...     return w
...

>>> # A complete bipartite graph with 4 nodes and 4 edges
... B = nx.complete_bipartite_graph(2, 2)
... # Add some arbitrary weight to the edges
... for i, (u, v) in enumerate(B.edges()):
...     B.edges[u, v]["weight"] = i + 1
...

>>> for edge in B.edges(data=True):
...     print(edge)
...
(0, 2, {'weight': 1})
(0, 3, {'weight': 2})
(1, 2, {'weight': 3})
(1, 3, {'weight': 4})

>>> # By default, the weight is the number of shared neighbors
... G = bipartite.generic_weighted_projected_graph(B, [0, 1])
... print(list(G.edges(data=True)))
[(0, 1, {'weight': 2})]

>>> # To specify a custom weight function use the weight_function parameter
... G = bipartite.generic_weighted_projected_graph(
...     B, [0, 1], weight_function=jaccard
... )
... print(list(G.edges(data=True)))
[(0, 1, {'weight': 1.0})]

>>> G = bipartite.generic_weighted_projected_graph(
...     B, [0, 1], weight_function=my_weight
... )
... print(list(G.edges(data=True)))
[(0, 1, {'weight': 10})]

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.overlap_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