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The following matrices find their main application in graph and network theory. Adjacency matrix — a square matrix representing a graph, with aij non-zero if vertex i and vertex j are adjacent. Biadjacency matrix — a special class of adjacency matrix that describes adjacency in bipartite graphs. Degree matrix — a diagonal matrix defining the degree of each vertex in a graph. Edmonds matrix — a square matrix of a bipartite graph. Incidence matrix — a matrix representing a relationship between two classes of objects (usually vertices and edges in the context of graph theory). Laplacian matrix — a matrix equal to the degree matrix minus the adjacency matrix for a graph, used to find the number of spanning trees in the graph. Seidel adjacency matrix — a matrix similar to the usual adjacency matrix but with −1 for adjacency; +1 for nonadjacency; 0 on the diagonal. Tutte matrix — a generalisation of the Edmonds matrix for a balanced bipartite graph. |
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