For *d*=2 the resulting graph is a (*q*+1)-coclique.
For *d*>2 this graph is strongly regular, with parameters
*v* = (*q*^{d} − 1)/(*q* − 1),
*k* = *q*(*q*^{d−2} − 1)/(*q* − 1),
λ = q^{2}(*q*^{d−4} − 1)/(*q* − 1) +
*q* − 1,
μ = (*q*^{d−2} − 1)/(*q* − 1).

A projective line is totally isotropic if it induces a clique in this graph,
and conversely every edge spans a totally isotropic line, so that the graph
is the collinearity graph of the polar space formed by the projective points
and the totally isotropic lines.
In particular, the graph Sp(4,*q*) is the collinearity graph of a
generalized quadrangle with parameters GQ(*q*,*q*).
See also GQ(2,2).