  The emergence of explosive synchronization has been reported as an abrupt
transition in complex networks of first-order Kuramoto oscillators. In this
Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform
a cascade of transitions toward a synchronous macroscopic state, which is a
novel phenomenon that we call \textit{cluster explosive synchronization}. We
provide a rigorous analytical treatment using a mean-field analysis in
uncorrelated networks. Our findings are in good agreement with numerical
simulations and fundamentally deepen the understanding of microscopic
mechanisms toward synchronization.
