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Adjacency matrix
In mathematics and computer science, the adjacency matrix of a finite directed or undirected graph G on n vertices is the n Ă— n matrix where the nondiagonal entry a_{ij} is the number of edges from vertex i to vertex j, and the diagonal entry a_{ii} is either twice the number of loops at vertex i or just the number of loops (usages differ, depending on the mathematical needs; this article follows the former convention for undirected graphs, though directed graphs always follow the latter). There exists a unique adjacency matrix for each graph (up to permuting rows and columns), and it is not the adjacency matrix of any other graph.
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