  We introduce an easily computable topological measure which locates the
effective crossover between segregation and integration in a modular network.
Segregation corresponds to the degree of network modularity, while integration
is expressed in terms of the algebraic connectivity of an associated
hyper-graph. The rigorous treatment of the simplified case of cliques of equal
size that are gradually rewired until they become completely merged, allows us
to show that this topological crossover can be made to coincide with a
dynamical crossover from cluster to global synchronization of a system of
coupled phase oscillators. The dynamical crossover is signaled by a peak in the
product of the measures of intra-cluster and global synchronization, which we
propose as a dynamical measure of complexity. This quantity is much easier to
compute than the entropy (of the average frequencies of the oscillators), and
displays a behavior which closely mimics that of the dynamical complexity index
based on the latter. The proposed toplogical measure simultaneously provides
information on the dynamical behavior, sheds light on the interplay between
modularity vs total integration and shows how this affects the capability of
the network to perform both local and distributed dynamical tasks.
