This graph is the complement of the Johnson graph $\mathrm{J}(13,2)$.
| Number of vertices: | $78$ |
| Diameter: | $2$ |
| Intersection array: | $\{55,18;1,45\}$ |
| Spectrum: | $55^1 1^{65} (-10)^{12}$ |
| Automorphism group: | $\mathrm{S}_{13}$ |
| Distance-transitive: | Yes |
| Primitive |