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Evolving Apollonian networks with small-world scale-free topologies
Zhongzhi Zhang1, Lili Rong, Shuigeng Zhou
1Department of Computer Science and Engineering, Fudan University, Shanghai 200433, China. xinjizzz@sina.com
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
Summary
We introduce evolutionary Apollonian networks (EANs) and general deterministic Apollonian networks (GDANs), which exhibit power-law distributions and small-world properties. These evolving networks demonstrate tunable exponents and collective synchronization behaviors.
Area of Science:
- Network Science
- Complex Systems
- Statistical Physics
Background:
- Evolving networks are crucial models for understanding complex systems.
- Apollonian networks offer a unique framework for network generation.
- Characterizing the properties of evolving network models is essential.
Purpose of the Study:
- To introduce and analyze two novel types of evolving networks: EANs and GDANs.
- To investigate their structural and dynamical properties.
- To explore their potential for modeling complex systems.
Main Methods:
- Development of simple iteration algorithms for network generation.
- Conducting simulations to observe network behavior.
- Employing theoretical analysis for mathematical predictions.
Main Results:
- Both EANs and GDANs exhibit power-law degree distributions with tunable exponents (2-3).
- Accurate expressions for the clustering coefficient were derived for both network types.
- Analysis revealed small-world characteristics (short average path length and small diameter).
- Collective synchronization was investigated on EANs.
Conclusions:
- EANs and GDANs are robust evolving network models with tunable properties.
- These networks possess small-world features, making them suitable for various applications.
- Further research into synchronization on EANs is warranted.
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