  We investigate the dynamical role of inhibitory and highly connected nodes
(hub) in synchronization and input processing of leaky-integrate-and-fire
neural networks with short term synaptic plasticity. We take advantage of a
heterogeneous mean-field approximation to encode the role of network structure
and we tune the fraction of inhibitory neurons $f_I$ and their connectivity
level to investigate the cooperation between hub features and inhibition. We
show that, depending on $f_I$, highly connected inhibitory nodes strongly drive
the synchronization properties of the overall network through dynamical
transitions from synchronous to asynchronous regimes. Furthermore, a metastable
regime with long memory of external inputs emerges for a specific fraction of
hub inhibitory neurons, underlining the role of inhibition and connectivity
also for input processing in neural networks.
