Definition 2.1 (Adjacency matrix). The adjacency matrix of a graph $G$ is the matrix $A_{G} : V \times V \to ℝ$ defined by

A_{G} (x, y) = {\begin{matrix} 1 & {x, y} \in E (G) \\ 0 & {x, y} \notin E (G) \end{matrix}