How to graph adjacency matrix using MATLAB

Question

I want to create a plot showing connections between nodes from an adjacency matrix like the one below.

Answer 1

If your graph is connected, a way to construct the array xy to pass to gplot is as v(:,[2 3]) where v is the matrix of eigenvectors of the Laplacian matrix, ordered from smallest eigenvalues to largest. So we can do it this way:

L=diag(sum(A))-A;
[v,~]=eig(L);
xy=v(:,[2 3])
gplot(A,xy)

or this way:

L=diag(sum(A))-A;
[v,~]=eigs(L,3,'SM')
xy=v(:,[2 1])
gplot(A,xy)

The second one should be more efficient, especially if A is big.

This will create a nice plot under normal circumstances. This is not guaranteed to work; in particular, it is not guaranteed to assign different nodes different coordinates. But usually it works pretty nicely.

Some theory behind this can be found at https://arxiv.org/pdf/1311.2492.pdf