We can encode community information to this type of plot by colouring the nodes according to the communitiy memberships.

\begin{equation*}
A_{ij} = \left\{
\begin{array}{lr}
1 & : \text{if }i\text{ connected to }j\\
0 & : \text{otherwise}
\end{array}
\right.
\end{equation*}

The usefulness of the adjacency matrix visualisation depends largely on the order of the rows and columns in the plot. By finding communities in the network, we can reorder the rows and columns of the adjacency matrix accordingly to produce a plot that looks as follows: