The cyclotomic graph of order 
with 
a prime power is a graph on
nodes with two nodes adjacent if their
difference is a cube in the finite field GF(
). This graph is undirected when 
. Simple cyclotomic graphs
therefore exist for orders 4, 7, 13, 16, 19, 25, 31, 37, 43, 49, 61, 64, 67, 73,
79, 97, ... (OEIS A137827).
The cyclotomic graphs are cubic analogs of the Paley graphs.
For 
a prime, cyclotomic graphs are also circulant graphs 
with parameters 
given by the cubes (mod 
).
Special case of cyclotomic graphs are summarized in the table below.
 | graph |
| 4 | 2-ladder rung graph |
| 7 | cycle graph  |
| 16 | Clebsch graph |
| 25 | rook graph  |
