  We introduce a condition for an ensemble of networked phase oscillators to
feature an abrupt, first-order phase transition from an unsynchronized to a
synchronized state. This condition is met in a very wide spectrum of
situations, and for various oscillators' initial frequency distributions. We
show that the occurrence of such transitions is always accompanied by the
spontaneous emergence of frequency-degree correlations in random network
architectures. We also discuss ways to relax the condition, and to further
extend the possibility for the first-order transition to occur, and illustrate
how to engineer magnetic-like states of synchronization. Our findings thus
indicate how to search for abrupt transitions in real-world applications.
