Finding the number of paths of given length in a undirected unweighted graph

Question

\'Length\' of a path is the number of edges in the path.

Given a source and a destination vertex, I want to find the number of paths form the s

Answer 1

So, here's a nifty graph theory trick that I remember for this one.

Make an adjacency matrix A. where A[i][j] is 1 if there is an edge between i and j, and 0 otherwise.

Then, the number of paths of length k between i and j is just the [i][j] entry of A^k.

So, to solve the problem, build A and construct A^k using matrix multiplication (the usual trick for doing exponentiation applies here). Then just look up the necessary entry.

EDIT: Well, you need to do the modular arithmetic inside the matrix multiplication to avoid overflow issues, but that's a much smaller detail.