Matriks Graph

    In mathematics and computer science, an adjacency matrix is a means of representing which vertices (or nodes) of a graph are adjacent to which other vertices. Another matrix representation for a graph is the incidence matrix.
Specifically, the adjacency matrix of a finite graph G on n vertices is the n × n matrix where the non-diagonal entry a_ij is the number of edges from vertex i to vertex j, and the diagonal entry a_ii, depending on the convention, is either once or twice the number of edges (loops) from vertex i to itself.In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected, the adjacency matrix is symmetric.The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.

Examples

The convention followed here is that an adjacent edge counts 1 in the matrix for an undirected graph.

·      The adjacency matrix of a complete graph is all 1's except for 0's on the diagonal.

·      The adjacency matrix of an empty graph is a zero matrix.