This graph is the complement of the Johnson graph $\mathrm{J}(23,2)$.
| Number of vertices: | $253$ |
| Diameter: | $2$ |
| Intersection array: | $\{210,38;1,190\}$ |
| Spectrum: | $210^1 1^{230} (-20)^{22}$ |
| Automorphism group: | $\mathrm{S}_{23}$ |
| Distance-transitive: | Yes |
| Primitive |