  Cortical regions without direct neuronal connections have been observed to
exhibit synchronized dynamics. A recent empirical study has further revealed
that such regions that share more common neighbors are more likely to behave
coherently. To analytically investigate the underlying mechanisms, we consider
that a set of n oscillators, which have no direct connections, are linked
through m intermediate oscillators (called mediators), forming a complete
bipartite network structure. Modeling the oscillators by the Kuramoto-Sakaguchi
model, we rigorously prove that mediated remote synchronization, i.e.,
synchronization between those n oscillators that are not directly connected,
becomes more robust as the number of mediators increases. Simulations are also
carried out to show that our theoretical findings can be applied to other
general and complex networks.
