Synchronization of Modular Network

Synchronization of Modular Network

We first review some characteristics of synchronization occurring in modular complex networks and discuss the interplay between the synchronization and the module detection algorithm. From this perspective, we introduce a modified Kuramoto model with a gauge term depending on the link betweenness centrality (BC). The gauge term drives the phase difference between two nodes from 0 to π as BC increases from minimum to maximum. The system governed by this model exhibits a phase synchronization within each module, but not globally. The average velocities of each module are different. Since such behavior is obtained in a steady state, the model is useful for detecting modules in the context of synchronization without any characteristic time as needed in previous module detection algorithms.

We first review some characteristics of synchronization occurring in modular complex networks and discuss the interplay between the synchronization and the module detection algorithm. From this perspective, we introduce a modified Kuramoto model with a gauge term depending on the link betweenness centrality (BC). The gauge term drives the phase difference between two nodes from 0 to π as BC increases from minimum to maximum. The system governed by this model exhibits a phase synchronization within each module, but not globally. The average velocities of each module are different. Since such behavior is obtained in a steady state, the model is useful for detecting modules in the context of synchronization without any characteristic time as needed in previous module detection algorithms.