Synchronization on community networks

Abstract

In this Letter, we propose a growing network model that can generate scale-free networks with a tunable community strength. The community strength, $C$, is directly measured by the ratio of the number of external edges to internal ones; a smaller $C$ corresponds to a stronger community structure. According to the criterion obtained based on the master stability function, we show that the synchronizability of a community network is significantly weaker than that of the original Barabási-Albert network. Interestingly, we found an unreported linear relationship between the smallest nonzero eigenvalue and the community strength, which can be analytically obtained by using the combinatorial matrix theory. Furthermore, we investigated the Kuramoto model and found an abnormal region ($C\le 0.002$), in which the network has even worse synchronizability than the uncoupled case (C=0). On the other hand, the community effect will vanish when $C$ exceeds 0.1. Between these two extreme regions, a strong community structure will hinder global synchronization.

4 figures and 4 pages

References in corpus (17)

• The structure and function of complex networks
• Community structure in social and biological networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Defining and identifying communities in networks
• Synchronization in small-world systems
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Universality in the synchronization of weighted random networks
• Factors that predict better synchronizability on complex networks
• Modular synchronization in complex networks
• Clustering and Synchronization of Oscillator Networks
• Collective synchronization induced by epidemic dynamics on complex networks with communities
• Enhance synchronizability by structural perturbations
• Relations between Average Distance, Heterogeneity and Network Synchronizability
• Better Synchronizability Predicted by Crossed Double Cycle
• Better synchronizability predicted by a new coupling method
• The synchronizability of highly clustered scale-free networks
• Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings

Cited by in corpus (10)

• Synchronization in complex networks
• Predicting Missing Links via Local Information
• Epidemic spreading on modular networks: The fear to declare a pandemic
• Community consistency determines the stability transition window of power-grid nodes
• Multi-resolution community detection based on generalized self-loop rescaling strategy
• Broad lifetime distributions for ordering dynamics in complex networks
• The development of generalized synchronization on complex networks
• A Unified Method of Detecting Core-Periphery Structure and Community Structure in Networks
• Finding Community Structure Based on Subgraph Similarity
• Detecting network communities via greedy expanding based on local superiority index