This graph is the complement of the Johnson graph $\mathrm{J}(36,2)$.
| Number of vertices: | $630$ |
| Diameter: | $2$ |
| Intersection array: | $\{561,64;1,528\}$ |
| Spectrum: | $561^1 1^{594} (-33)^{35}$ |
| Automorphism group: | $\mathrm{S}_{36}$ |
| Distance-transitive: | Yes |
| Primitive |