  In the field of complex networks and graph theory, new results are typically
tested on graphs generated by a variety of algorithms such as the
Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most
graph generating algorithms do not typically create graphs with symmetries,
which have been shown to have an important role on the network dynamics. Here,
we present an algorithm to generate graphs with prescribed symmetries. The
algorithm can also be used to generate graphs with a prescribed equitable
partition but possibly without any symmetry. We also use our graph generator to
examine the recently raised question about the relation between the orbits of
the automorphism group and a graph's minimal equitable partition.
