Tensor Product Edge Count

Problem

Compute the number of edges in the tensor (categorical) product G1 x G2 of two undirected graphs.

An edge exists in the product exactly when both coordinates change along an edge, so each pair of factor edges yields two directed edges, or 2 * m1 * m2 total undirected edges. Return the count.

Hint

Every pair of edges in the factors produces two product edges, one per orientation.

Test cases

case 1

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

expected: 4

case 2

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

expected: 4

case 3

in: [[],[[0,1]]]

expected: 0

case 4

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

expected: 6

Starter codePython

def tensor_product_edges(edges1, edges2):
    # Your code here
    pass

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