  Dynamical processes occurring on top of complex networks have become an
exciting area of research. Quenched disorder plays a relevant role in general
dynamical processes and phase transitions, but the effect of topological
quenched disorder on the dynamics of complex networks has not been
systematically studied so far. Here, we provide heuristic and numerical
analyses of the contact process defined on some complex networks with
topological disorder. We report on Griffiths phases and other rare region
effects, leading rather generically to anomalously slow relaxation in
generalized small-world networks. In particular, it is illustrated that
Griffiths phases can emerge as the consequence of pure topological
heterogeneity if the topological dimension of the network is finite.
