# Adjacency matrix format (graph)

Given a simple undirected graph $G = (V,E)$ we can define the adjacency matrix $M$ of size $\vert V \vert \times \vert V \vert$ as follows:

$$ M_{i,j} = \begin{cases} 1 & \text{if } (i,j) \in E \text{ or } (j,i) \in E\\ 0 & \text{otherwise} \end{cases} $$

(This can be extended to directed graphs by removing the check for both directions.) For undirected graphs this is a symmetric matrix.