  In algebraic geometry, superspecial curves are important research objects.
While the number of superspecial genus-3 curves in characteristic $p$ is known,
the number of hyperelliptic ones among them has not been determined even for
small $p$. In this paper, in order to compute the latter number, we give an
algorithm for computing the Richelot isogeny graph of superspecial abelian
threefolds by using theta functions. Our algorithm enables us to efficiently
list superspecial genus-3 curves, and we succeeded in counting hyperelliptic
curves among them when $11 \leq p < 100$ by executing our algorithm in Magma.
