  Complex networks are abundant in nature and many share an important
structural property: they contain a few nodes that are abnormally highly
connected (hubs). Some of these hubs are called influencers because they couple
strongly to the network and play fundamental dynamical and structural roles.
Strikingly, despite the abundance of networks with influencers, little is known
about their response to stochastic forcing. Here, for oscillatory dynamics on
influencer networks, we show that subjecting influencers to an optimal
intensity of noise can result in enhanced network synchronization. This new
network dynamical effect, which we call coherence resonance in influencer
networks, emerges from a synergy between network structure and stochasticity
and is highly nonlinear, vanishing when the noise is too weak or too strong.
Our results reveal that the influencer backbone can sharply increase the
dynamical response in complex systems of coupled oscillators.
