How to determine whether two graphs are isomorphic from larger adjacency matrices

Solution 1:

I don't think there is an easy way of doing it since graph ismorphism is a hard problem (it's not know which class it's in) .

however there are a couple of heuristics to help, counting degrees, matching by degrees, counting loops, or finding any kind of pattern

in your example in the second matrix it's clear that the graph is bipartite with one side having being the odd indexed nodes and the other the even indexed nodes (notice that there is only two different rows that keep repeating), however the first graph is clearly not bipartite so the answer is easy.