[1][2] It is a strongly regular graph with 16 vertices and 48 edges, with each vertex having degree 6.

In the Shrikhande graph, any two vertices I and J have two distinct neighbors in common (excluding the two vertices I and J themselves), which holds true whether or not I is adjacent to J.

This equality implies that the graph is associated with a symmetric BIBD.

[2][3] The Shrikhande graph is locally hexagonal; that is, the neighbors of each vertex form a cycle of six vertices.

As with any locally cyclic graph, the Shrikhande graph is the 1-skeleton of a Whitney triangulation of some surface; in the case of the Shrikhande graph, this surface is a torus in which each vertex is surrounded by six triangles.

The embedding forms a regular map in the torus, with 32 triangular faces.

[5] The automorphism group of the Shrikhande graph is of order 192.

It acts transitively on the vertices, on the edges and on the arcs of the graph.