Weighted Bimodal Bipartite Graph Projection conserving original weights

Question

I have a large ( 36k vertices, 50k edges ) weighted bimodal bipartite graph and I would like to generate a projection that not only count the neighbors like the default weighted implementation but also sum the weights on the edges. You can think of it as a bipartite graph containing black vertices and blue vertices, where I want to conserve the original graph weights when there are only blue vertices.

The implementations I came across keep the orange value, I am interested on the red one (or hopefully get a bi-weighted projection).

I've looked so far in igraph, networkx and python-tool but in so far I only observed the projection counting the amount of edges.

Networkx method generic_weighted_projected_graph(B, nodes, weight_function=None) may make this viable but I can't see how (sna is new to me, although I am an so so python user).

Answer 1

There is an example in the documentation you reference at https://networkx.github.io/documentation/latest/reference/generated/networkx.algorithms.bipartite.projection.generic_weighted_projected_graph.html of how to do exactly this.

It goes like this:

import networkx as nx
from networkx.algorithms import bipartite

edges = [('A1','B1',3),
         ('A1','B2',7),
         ('A2','B1',2),
         ('A2','B2',4),
         ]

B = nx.Graph()
B.add_weighted_edges_from(edges)

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

G = bipartite.generic_weighted_projected_graph(B, ['A1', 'A2'], weight_function=my_weight)


print G.edges(data=True)

output

[('A1', 'A2', {'weight': 16})]