Say there is a task to determine whether two graphs are isomorphic, given a picture of the graphs. However the graphs are really complex, with a lot of vertices and edges, and things like number of vertices or edges and degrees are the same and it is really difficult to count triangles, or any other cycle, or to find what to swap. What to do then?
Sometimes I spend about 4 hours to find an isomorphism, so I was thinking : is there some more efficient way? Can maybe the adjacency matrix help?
The Wikipedia article on graph isomorphism problem has pretty extensive discussion, describing the state of the art, practical algorithms, solved special cases etc.