Synchronization and modularity in complex networks
arXiv:cond-mat/0610726 · doi:10.1140/epjst/e2007-00066-2
Abstract
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the partition these patterns provide. The results indicate that the more stable the patterns are, the larger tends to be the modularity of the partition defined by them. This correlation works pretty well in homogeneous networks (all nodes have similar connectivity) but fails when networks contain hubs, mainly because the modularity is never improved where isolated nodes appear, whereas in the synchronization process the characteristic of hubs is to have a large stability when forming its own community.
To appear in the Proceedings of Workshop on Complex Systems: New Trends and Expectations, Santander, Spain, 5-9 June 2006
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- Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
- Global synchronization of partially forced Kuramoto oscillators on Networks
- Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators
- Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity
- A Model for Image Segmentation in Retina
- Communities and Patterns of Scientific collaboration
- Network community detection via iterative edge removal in a flocking-like system