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A Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.

David Shui Wing Hui¹, Yi-Chao Chen¹, Gong Zhang¹

¹Huawei Technologies Co. Ltd., Hong Kong, China.

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Summary

A novel Markov chain model unifies complex network evolution, accurately capturing degree distribution "trichotomy" and outperforming classical models in real-world applications like social networks.

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Area of Science:

Network Science
Mathematical Modeling
Complex Systems

Background:

Complex networks exhibit diverse degree distributions.
Existing models struggle to capture the "trichotomy" in these distributions.
A unified framework is needed for network evolution analysis.

Purpose of the Study:

To introduce a unified Markov chain model for complex network evolution.
To address the formation mechanism underlying degree distribution "trichotomy".
To derive closed-form solutions for network properties.

Main Methods:

Development of a novel Markov chain model.
Incorporation of a mechanism to explain degree distribution "trichotomy".
Derivation of closed-form solutions for network analysis.

Main Results:

The proposed model successfully captures the "trichotomy" in degree distributions.
The unified framework encompasses classical models like Poisson, Exponential, and Power-law.
Simulations and experimental results show superior performance against classical models.

Conclusions:

The Markov chain model provides a superior, unified framework for complex network evolution.
The model's ability to address "trichotomy" offers new insights into network formation.
Applications span citation analysis, social networks, and vehicular network design.