The cyclotomic graph of order 
with 
a prime power is a graph
on 
nodes with two nodes adjacent if their difference
is a cubic number in the finite
field 
.
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 number, cyclotomic graphs are also circulant
graphs 
with parameters 
given by the cubes (mod 
).
Special cases of cyclotomic graphs are summarized in the table below.
 | graph |
| 4 | 2-ladder rung graph |
| 7 | cycle
graph  |
| 16 | Clebsch graph |
| 25 | rook
graph  |
