This graph is the complement of the Johnson graph $\mathrm{J}(37,2)$.
| Number of vertices: | $666$ |
| Diameter: | $2$ |
| Intersection array: | $\{595,66;1,561\}$ |
| Spectrum: | $595^1 1^{629} (-34)^{36}$ |
| Automorphism group: | $\mathrm{S}_{37}$ |
| Distance-transitive: | Yes |
| Primitive |