Average distance as a predictor of synchronisability in networks of coupled oscillators

The importance of networks of coupled oscillators is widely recognized. Such networks occur in biological systems like the heart, in chemical systems, in computational problems, and in engineering systems. Systems of coupled oscillators can also be used as an abstract model for synchronisation in organisations. Here we show that synchronisability in a specific coupledoscillator model, the Kuramoto model, is best predicted using the average distance (or characteristic path length) between nodes in the network. We do this by simulating the Kuramoto dynamics on a collection of networks of varying type, including Random, Small-World, and ScaleFree networks. Furthermore, we show that, for several real-world networks, a simple estimate based on the average distance can predict the coupling required for networks to synchronise within a threshold time. .