The vertices of this graph are the 100 cocliques of size 15 in the Hoffman–Singleton graph, two cocliques being adjacent when they have 8 points in common.
| Number of vertices: | $100$ |
| Diameter: | $4$ |
| Intersection array: | $\{15,14,10,3;1,5,12,15\}$ |
| Spectrum: | $15^1 5^{21} 0^{56} (-5)^{21} (-15)^{21}$ |
| Automorphism group: | $\mathrm{P} \Sigma \mathrm{U}(3,5^2)$ |
| Distance-transitive: | Yes |
| Bipartite |