In mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.
The Seidel matrix of G is also the adjacency matrix of a signed complete graph KG in which the edges of G are negative and the edges not in G are positive.
It is also the adjacency matrix of the two-graph associated with G and KG.
The eigenvalue properties of the Seidel matrix are valuable in the study of strongly regular graphs.
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