Splitting a network into connected components

A function to return all the components of a graph

This function returns the components of a graph represented by an adjacency matrix A. The idea is based on the fact that each element (i,j) in A^n represents the number of paths of size n from node i to node j. Extending this to all powers upto N where N is the number of nodes in the graph, it can be said that two nodes are in the same component iff the (i,j) element in S = A+A^2+A^3....+A^n is not zero. S can be worked out to be inv(I-A)*(A-A^(n+1)). It must be pointed out that even if A is sparse, there is no guarantee that A^(n+1) will also be sparse, so there is no use in exploiting MATLAB's sparse matrix functionality.