Betweenness Centrality (Brandes-lite)

Problem

Compute the (unnormalized) betweenness centrality of every node in an undirected unweighted graph.

For each ordered source, accumulate dependencies with Brandes' algorithm: when a shortest path has sigma[w] prefixes reaching w and sigma[v] via v, node v receives (sigma[v] / sigma[w]) * (1 + delta[w]). Sum over all sources and divide by 2 for the undirected pairs. Return floats in node order.

Hint

Accumulate dependency contributions while unwinding the BFS stack, deepest nodes first.

Test cases

case 1

in: [3,[[0,1],[1,2]]]

expected: [0,1,0]

case 2

in: [4,[[0,1],[0,2],[0,3]]]

expected: [3,0,0,0]

case 3

in: [4,[[0,1],[1,2],[2,3],[3,0]]]

expected: [0.5,0.5,0.5,0.5]

case 4

in: [4,[[0,1],[1,2],[2,3]]]

expected: [0,2,2,0]

case 5

in: [3,[[0,1],[1,2],[2,0]]]

expected: [0,0,0]

Starter codePython

def betweenness_centrality(n, edges):
    # Your code here
    pass

5 test cases · run your code against them in the editor