A dynamical approach to identify vertices' centrality in complex networks

In this paper, we proposed a dynamical approach to assess vertices' centrality according to the synchronization process of the Kuramoto model. In our approach, the vertices' dynamical centrality is calculated based on the Difference of vertices' Synchronization Abilities (DSA), which are different from traditional centrality measurements that are related to the topological properties. Through applying our approach to complex networks with a clear community structure, we have calculated all vertices' dynamical centrality and found that vertices at the end of weak links have higher dynamical centrality. Meanwhile, we analyzed the robustness and efficiency of our dynamical approach through testing the probabilities that some known vital vertices were recognized. Finally, we applied our dynamical approach to identify community due to its satisfactory performance in assessing overlapping vertices. Our present work provides a new perspective and tools to understand the crucial role of heterogeneity in revealing the interplay between the dynamics and structure of complex networks.