Graphs can be represented using the adjacency matrix $A \in {\rm I\!R} ^{|\mathcal{V}| \times |\mathcal{V}| }$

Each node in the graph has a row and a column in the adjacency matrix.

The presence of edges is represented as an entry in the matrix as $A[u,v] = 1$ if $(u,v) \in \mathcal{E}$ and $A[u,v] = 0$ otherwise