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AdjacencyMatrix—Wolfram Documentation

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As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

AdjacencyMatrix[g]

gives the SparseArray object representing the graph g.

AdjacencyMatrix[g,n]

gives the SparseArray object representing the graph g, adding additional unconnected vertices, if necessary, to create a graph with n vertices.

Details and Options

AdjacencyMatrix functionality is now available in the built-in Wolfram Language function AdjacencyMatrix.
To use AdjacencyMatrix, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
The graph g can be specified by a rule list, an adjacency matrix, or the Combinatorica representation of a graph.
The rows/columns of the SparseArray object correspond to vertices in the order returned by VertexList[g].

Examplesopen all close all Basic Examples (2)

The adjacency matrix of a graph specified by a rule list:

This function has been superseded by AdjacencyMatrix in the Wolfram System:

Scope (2)

The SparseArray representation of a graph specified by a rule list:

This adds an extra row and column to the adjacency matrix, corresponding to unconnected vertices:

Properties & Relations (2)

This gives a SparseArray representation of a graph specified by a Combinatorica object:

This shows the MatrixPlot of the adjacency matrix of a GridGraph, and its graph drawing:

Possible Issues (1)

A second argument specifying fewer vertices than those contained in the graph is ignored:

Wolfram Research (2007), AdjacencyMatrix, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/AdjacencyMatrix.html. Text Wolfram Research (2007), AdjacencyMatrix, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/AdjacencyMatrix.html.CMS Wolfram Language. 2007. "AdjacencyMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/AdjacencyMatrix.html.APA Wolfram Language. (2007). AdjacencyMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/AdjacencyMatrix.htmlBibTeX @misc{reference.wolfram_2025_adjacencymatrix, author="Wolfram Research", title="{AdjacencyMatrix}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/AdjacencyMatrix.html}", note=[Accessed: 17-August-2025]}BibLaTeX @online{reference.wolfram_2025_adjacencymatrix, organization={Wolfram Research}, title={AdjacencyMatrix}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/AdjacencyMatrix.html}, note=[Accessed: 17-August-2025]}

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