  The replicator equation is one of the fundamental tools to study evolutionary
dynamics in well-mixed populations. This paper contributes to the literature on
evolutionary graph theory, providing a version of the replicator equation for a
family of connected networks with communities, where nodes in the same
community have the same degree. This replicator equation is applied to the
study of different classes of games, exploring the impact of the graph
structure on the equilibria of the evolutionary dynamics.
