Circulant graphs

A circulant graph is a graph on n nodes, which we can take to be
numbers mod n. For every element of an index set (which without loss
of generality we can take to run from 1 to floor(n/2)) we draw an edge
from
m to m+i if i is in the index set. A circulant graph has a circulant
matrix as its adjacency matrix, and from the size of the index set
there are 2^floor(n/2) of them for each n. If the index set represents
consonances for an n-division, the corresponding circulant graph has a
musical interpretation.

Circulant matricies can have nontrivial isomorphisms. For instance
there are 64 circulant matricies mod 12, but only 48 if we take them
up to isomorphism. Nontrivial isomorphisms could be interesting.