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