  We search for conditions under which a characteristic time scale for ordering
dynamics towards either of two absorbing states in a finite complex network of
interactions does not exist. With this aim, we study random networks and
networks with mesoscale community structure built up from randomly connected
cliques. We find that large heterogeneity at the mesoscale level of the network
appears to be a sufficient mechanism for the absence of a characteristic time
for the dynamics. Such heterogeneity results in dynamical metastable states
that survive at any time scale.
