[5] It is constructed from the Steiner system (3, 6, 22) by representing its 77 blocks as vertices and joining two vertices iff they have no terms in common or by deleting a vertex and its neighbors from the Higman–Sims graph.

[6][7] For any term, the family of blocks that contain that term forms an independent set in this graph, with 21 vertices.

In a result analogous to the Erdős–Ko–Rado theorem (which can be formulated in terms of independent sets in Kneser graphs), these are the unique maximum independent sets in this graph.

[4] It is one of seven known triangle-free strongly regular graphs.

[8] Its graph spectrum is (−6)21255161,[6] and its automorphism group is the Mathieu group M22.