  The emergence of synchronized behavior is a direct consequence of networking
dynamical systems. Naturally, strict instances of this phenomenon, such as the
states of complete synchronization are favored, or even ensured, in networks
with a high density of connections. Conversely, in sparse networks, the system
state-space is often shared by a variety of coexistent solutions. Consequently,
the convergence to complete synchronized states is far from being certain. In
this scenario, we report the surprising phenomenon in which completely
synchronized states are made the sole attractor of sparse networks by removing
network links, the sparsity-driven synchronization. This phenomenon is observed
numerically for nonlocally coupled Kuramoto networks and verified analytically
for locally coupled ones. In addition, we reduce the network equations to a
one-dimension dynamical system to unravel the bifurcation scenario underlying
the network transition to completely synchronized behavior. Furthermore, we
present a simple procedure, based on the bifurcations in the thermodynamic
limit, that determines the minimum number of links to be removed in order to
ensure complete synchronization. Finally, we propose an application of the
reported phenomenon as a control scheme to drive complete synchronization in
high connectivity networks.
