This graph is the complement of the Johnson graph $\mathrm{J}(18,2)$.
| Number of vertices: | $153$ |
| Diameter: | $2$ |
| Intersection array: | $\{120,28;1,105\}$ |
| Spectrum: | $120^1 1^{135} (-15)^{17}$ |
| Automorphism group: | $\mathrm{S}_{18}$ |
| Distance-transitive: | Yes |
| Primitive |