We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology and spectral graph analysis.
Arenas et al. REF studied the relationship between topological and community structure of complex networks using the Kuramoto model of synchronization.
Synchronization Reveals Topological Scales in Complex Networks
Physical Review Letters, vol. 96, 114102, (2006)
Physics Medicine