What do you think is the most efficient algorithm for checking whether a graph represented by an adjacency matrix is connected? In my case I'm also given the weights of each edge.
There is another question very similar to mine: How to test if a graph is fully connected and finding isolated graphs from an adjacency matrix
That answer seems to be good, except I don't really understand it. How does repeatedly squaring the matrix give information about its connectivity? There is another an answer that claims eigenvectors also give information about the connectivity of the graph, could anyone explain that as well?
I'm asking this because I don't have the background to understand the answers given, I'm just solving a problem that has to do with these topics. Searching around on google didn't give me an answer either, so hopefully someone can clear it up.