如何使用邻接矩阵检查两个图的同构？

Question

Is there any way to check for the isomorphism of two graphs using the adjacency matrix in a simple way?

If it is, then please let me know...

Answer 1

No polynomial-time algorithm is known for this problem, though many instances can be solved quickly in practice using a tool like nauty .

Answer 2

If they are isomorph only the labeling is different.

So sorting the rows of the matrix (and accordingly reorder he columns also(if you swap rows, you also need to swap the columns)) should lead to two exact equal matrices, if the graphs are isomorph.

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If you compare a lot of not isomorph graphs, you should make some quick-checks first. Like:

• they need to have the same number of entries in both matrices
• same number of rows for the same number of entries in both matrices

This way you can fail early (much cheaper than the sorting)