[2] Published in 1963, it is cospectral to the hypercube graph Q4.

[3][4] The Hoffman graph has many common properties with the hypercube Q4—both are Hamiltonian and have chromatic number 2, chromatic index 4, girth 4 and diameter 4.

It has book thickness 3 and queue number 2.

Despite not being vertex- or edge-transitive, the Hoffmann graph is still 1-walk-regular (but not distance-regular).

The characteristic polynomial of the Hoffman graph is equal to making it an integral graph—a graph whose spectrum consists entirely of integers.