This graph is the complement of the Johnson graph $\mathrm{J}(34,2)$.
| Number of vertices: | $561$ |
| Diameter: | $2$ |
| Intersection array: | $\{496,60;1,465\}$ |
| Spectrum: | $496^1 1^{527} (-31)^{33}$ |
| Automorphism group: | $\mathrm{S}_{34}$ |
| Distance-transitive: | Yes |
| Primitive |