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Given a directed graph $ G $ with $ n $ nodes, we can represent this graph using an adjacency matrix $ A $. The stochastic matrix $ S $ can be derived from the adjacency matrix using the following ...

This is a follow-up question to Characterisation of walk-equivalent digraphs. Question: Do there exists two directed graphs $G$ and $H$ consisting of the same number ($n$) of vertices, such that \...

We consider an unweighted directed simple graph, $G$, with a Hamiltonian cycle. Q. Assume that the adjacency matrix of $G$ is non-singular. Do the characteristic and minimal polynomials of the ...