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We introduce a model to study the effect of degree-frequency correlations onsynchronization in networks of coupled oscillators. Analyzing this model, wefind several remarkable characteristics. We find a stationary synchronizedstate that is (i) universal, i.e., the degree of synchrony, as measured by aglobal order parameter, is independent of network topology, and (ii) fullyphase-locked, i.e., all oscillators become simultaneously phase-locked despitehaving different natural frequencies. This state separates qualitativelydifferent behaviors for two other classes of correlations where, respectively,slow and fast oscillators can remain unsynchronized. We close by presentinganalysis of the dynamics under arbitrary degree-frequency correlations.

Effects of degree-frequency correlations on network synchronization: universality and full phase-locking