Construction principles for highly synchronizable sparse directed networks

In this Letter sparse directed interaction networks of heterogeneous Kuramoto oscillators that give rise to enhanced synchronization properties are generated and analyzed. The particular networks, which allow for the transition to full synchronization for the smallest coupling strength, i.e., optimal networks, are found to be very homogeneous in the in-degree distribution, but exhibit very skewed out-degree distributions. Various correlations between in- and out-degree structure, oscillator heterogeneity and component structure, which are linked to an enhanced synchronizability, are discussed.