In an unweighted graph:
For undirected graphs, the adjacency matrix is symmetric, meaning $a_{ij} = a_{ji}$ for all $i$ and $j$.
Consider the undirected graph above.
Its adjacency matrix would be:
\[ A = \begin{bmatrix} 0 & 1 & 0 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 1 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 1 & 0 \end{bmatrix} \]
The diagonal entries of an adjacency matrix for a simple graph (without self-loops) are always 0.
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