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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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Digraphs with unique walk of length $k$ between any two vertices
Let $G$ be a digraph such that there is an unique directed walk of length $k$ between any two vertices.
Equivalently, if $A$ is the adjacency matrix of $G$, then $A^k$ is the matrix with all entries $ …