This graph is the complement of the Johnson graph $\mathrm{J}(40,2)$.
| Number of vertices: | $780$ |
| Diameter: | $2$ |
| Intersection array: | $\{703,72;1,666\}$ |
| Spectrum: | $703^1 1^{740} (-37)^{39}$ |
| Automorphism group: | $\mathrm{S}_{40}$ |
| Distance-transitive: | Yes |
| Primitive |