Adjacency Matrix

graph-theory linear-algebra

Definition

Adjacency Matrix

An adjacency matrix is a square matrix used to represent a graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.

$$A=(a_{ij}{)}_{i,j}=1,\dots n\text{with}{a}_{ij}=\{\begin{array}{ll}1& \text{if}(v_i,v_j)\in E\\ 0& \text{else}\end{array}$$

For undirected graphs, the adjacency matrix is symmetric.