How to find a triangle inside a graph?

Question

Here is an exercise in the Algorithm Design Manual.

Consider the problem of determining whether a given undirected graph G = (V, E) contains a triangle

Answer 1

I really like the matrix multiplication solution discussed in this blog post.

Let a = the adjacency matrix

• The adjacencies in a*a (a2) matrix multiplied are the numbers of 2-length paths
• The adjacencies in a2*a matrix multiplied are the numbers of 3-length paths

The problem is, matrix multiplication is slow... However, you can use GPGPU to perform matrix multiplication and can have a performant solution on modern architectures that include a GPU.