  We investigate the emergence and persistence of communities through a
recently proposed mechanism of adaptive rewiring in coevolutionary networks. We
characterize the topological structures arising in a coevolutionary network
subject to an adaptive rewiring process and a node dynamics given by a simple
voterlike rule. We find that, for some values of the parameters describing the
adaptive rewiring process, a community structure emerges on a connected
network. We show that the emergence of communities is associated to a decrease
in the number of active links in the system, i.e. links that connect two nodes
in different states. The lifetime of the community structure state scales
exponentially with the size of the system. Additionally, we find that a small
noise in the node dynamics can sustain a diversity of states and a community
structure in time in a finite size system. Thus, large system size and/or local
noise can explain the persistence of communities and diversity in many real
systems.
