Matrices Used in Graph Theory
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.
Read more about this topic: List Of Matrices
Famous quotes containing the words graph and/or theory:
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)
“The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.”
—Thomas Henry Huxley (1825–95)