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An adjacency matrix is a square (0,1)-matrix used to represent a graph. Its entries indicate whether pairs of vertices are adjacent or not.
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Computing adjacency matrix eigenvalues by counting closed walks
Let $G$ be a finite undirected graph. A closed walk in $G$ is a walk from any vertex of $G$ to itself. It is relatively straightforward to show that the total number of closed walks of length $k$ in $ …