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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.

1 vote

Adjacency matrix of total graph

If $C$ is the incidence matrix (rows indexed by vertices, columns by edges, two 1s in each column) then $CC^T$ is the Laplacian matrix and $C^TC-2I is the adjacency matrix of the linegraph. From this …
Brendan McKay's user avatar
1 vote

Which directed graphs have a normal adjacency matrix?

For $n=1,\ldots,8$, the number of isomorphism classes of normal loop-free digraphs is apparently 1, 2, 5, 15, 49, 232, 1413, 14961. If loops are allowed, the counts for $n=1,\ldots,8$ are 2, 6, 22, 10 …
Brendan McKay's user avatar