Editing Adjacency matrix (section)

{{Short description|Square matrix used to represent a graph or network}}
In [[graph theory]] and [[computer science]], an '''adjacency matrix''' is a [[square matrix]] used to represent a finite [[graph (discrete mathematics)|graph]]. The elements of the [[matrix (mathematics)|matrix]] indicate whether pairs of [[Vertex (graph theory)|vertices]] are [[Neighbourhood (graph theory)|adjacent]] or not in the graph.

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 [[Glossary of graph theory terms#undirected|undirected]] (i.e. all of its [[Glossary of graph theory terms#edge|edges]] are bidirectional), the adjacency matrix is [[symmetric matrix|symmetric]]. 
The relationship between a graph and the [[eigenvalue]]s and [[eigenvector]]s of its adjacency matrix is studied in [[spectral graph theory]].

The adjacency matrix of a graph should be distinguished from its [[incidence matrix]], a different matrix representation whose elements indicate whether vertex–edge pairs are [[Incidence (graph)|incident]] or not, and its [[degree matrix]], which contains information about the [[degree (graph theory)|degree]] of each vertex.