  A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of
automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of
adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called
the unitary graphs, whose vertices are flags of the Hermitian unital and whose
adjacency relations are determined by certain elements of the underlying finite
fields. Such graphs admit the unitary groups as groups of automorphisms, and
they play a significant role in the classification of a family of symmetric
graphs with complete quotients such that an associated incidence structure is a
doubly point-transitive linear space. We give this classification in the paper
and also investigate combinatorial properties of the unitary graphs.
