AdjacencyGraph

AdjacencyGraph[amat]
gives the graph with adjacency matrix amat.

AdjacencyGraph[{v1,v2,},amat]
gives the graph with vertices and adjacency matrix amat.

Details and OptionsDetails and Options

Background
Background

  • AdjacencyGraph constructs a graph from an adjacency matrix representation of an undirected or directed graph. An adjacency matrix is a square matrix whose rows and columns correspond to the vertices of a graph and whose elements are non-negative integers that give the numbers of (directed) edges from vertex to vertex . Adjacency matrices with diagonal entries create self-loops.
  • The option DirectedEdges (with possible values Automatic, True, or False) may be used to control whether an undirected or directed graph is constructed. By default, AdjacencyGraph returns an undirected graph if the input matrix is symmetric and a directed graph otherwise.
  • AdjacencyGraph takes the same options as Graph (e.g. EdgeStyle, VertexStyle, EdgeLabels, VertexLabels, GraphLayout, VertexCoordinates, etc.). AdjacencyGraph does not take graph weights into account, so WeightedAdjacencyGraph must be used when constructing a graph from a weighted adjacency matrix.
  • AdjacencyList returns a list of vertices adjacent to a given vertex and therefore corresponds to a list of the positions of nonzero elements in the i^(th) column (and, in the case of undirected graphs, the i^(th) row) of the adjacency matrix. The entire adjacency matrix of any graph (including a graph constructed using AdjacencyGraph) may be returned using AdjacencyMatrix. IncidenceGraph uses an incidence matrix representation instead of an adjacency matrix to construct a graph.
Introduced in 2010
(8.0)