Expansion of a Set

Problem

Compute the edge expansion of a vertex subset S of an undirected graph: the number of edges crossing from S to its complement, divided by |S|.

Return 0.0 when S is empty or contains every node. edges is a list of [u, v] pairs and subset lists the nodes in S.

Hint

Small sets with many boundary edges are poor clusters.

case 1

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

expected: 0.5

case 2

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

expected: 1

case 3

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

expected: 2

case 4

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

expected: 0

case 5

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

expected: 0

Starter codePython

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

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