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Synchronizability of network ensembles with prescribed statistical properties
Shuguang Guan1, Xingang Wang, Kun Li
1Temasek Laboratories, National University of Singapore, 117508 Singapore.
Chaos (Woodbury, N.Y.)
|April 2, 2008
Summary
Network synchronizability depends on local structure, not just global properties. Homogeneous degree distribution enhances synchronizability in random networks, making extremely poor synchronizability rare.
Area of Science:
- Network Science
- Complex Systems
- Graph Theory
Background:
- Network synchronizability is crucial for system function.
- Global network properties alone do not determine synchronizability.
- Local network structure plays a significant role.
Purpose of the Study:
- To numerically investigate network synchronizability using spectral properties.
- To analyze the impact of local connection patterns on synchronizability.
- To examine synchronizability in network ensembles with specific statistical properties.
Main Methods:
- Numerical study of network ensembles.
- Analysis of spectral properties (eigenvalues and eigenratios).
- Comparison of network synchronizability across different ensembles with identical nodes and average degree.
Main Results:
- Eigenvalues and eigenratios for network synchronizability show well-defined distributions.
- Statistically, networks with extremely poor synchronizability are uncommon.
- Local connection patterns significantly influence network synchronizability.
- Degree homogeneity enhances synchronizability in random networks.
Conclusions:
- Network synchronizability is predominantly governed by local structure.
- Homogeneity of degree is a key factor in enhancing the synchronizability of random networks.
- Understanding local network topology is essential for predicting and controlling system synchrony.
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