There exist precisely three rank-3 strongly regular graphs on 169 vertices. They are $H(2,13)$, the Paley graph $P_{169}$, and the graph below which is the unique rank-3 $\mathrm{SRG}(169,72,31,30)$.
| Number of vertices: | $169$ |
| Diameter: | $2$ |
| Intersection array: | $\{72,40;1,30\}$ |
| Spectrum: | $72^1 7^{72} (-6)^{96}$ |
| Automorphism group: | $13^2:\left(3 \times \left(\mathrm{SL}_2(3):4\right)\right)$ |
| Distance-transitive: | Yes |
| Primitive |