is this betweenness calculation correct?

Question

I try to calculate betweenness for all nodes for the path from 2 to 6 in this simple graph.

G=nx.Graph()
edge=[(1,5),(2,5),(3,5),(4,5),(4,6),(5,7),(7,6)]
G.add_edges_from(edge)
btw=nx.betweenness_centrality_subset(G,[2],[6])

However the result is:

{1: 0.0, 5: 0.5, 2: 0.0, 3: 0.0, 4: 0.25, 6: 0.0, 7: 0.25}

I was wondering why the betweenness for node 5 is 0.5 while it should be 1 since the number of total shortest path is 2 and both of them include 5 and node 4 and 7 should be 0.5

Answer 1

It looks like a bug.

Here my guess. The bug seems coming from the _rescale function. Here, if the graph is indirected the computed values are multiplied by 0.5.

Since in the general betweenness_centrality a node is considered twice (shortest paths are computed for each node in the graph) for the betweenness_centrality_sub this is not necessary since shortest paths are only computed for the sources nodes.

Example:

nx.betweenness_centrality_subset(G,[2,6],[2,6])
# {1: 0.0, 5: 1.0, 2: 0.0, 3: 0.0, 4: 0.5, 6: 0.0, 7: 0.5}

So, if my guess is right, you just need to multiply by 2 the computed result.