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arXiv · 0901.1418

Degree-distribution Stability of Evolving Networks

Zhenting Hou·Xiangxing Kong·Dinghua Shi·Guanrong Chen·Qinggui Zhao
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Abstract

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.

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Zhenting Hou, Xiangxing Kong, Dinghua Shi, Guanrong Chen, Qinggui Zhao. 2009-04-23. Degree-distribution Stability of Evolving Networks. https://arxiv.org/abs/0901.1418

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