An Information Theory Approach to Network Evolution Models

IF 2.2 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of complex networks Pub Date : 2022-01-20 DOI:10.1093/comnet/cnac020

Amirmohammad Farzaneh, J. Coon

引用次数: 1

Abstract

A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called network evolution chain, is a stationary and ergodic stochastic process. Therefore, the asymptotic equipartition property can be applied to it. The model’s entropy rate and typical sequences are also explored. Extracting particular information from the network and methods to simulate network evolution in the continuous time domain are discussed. Additionally, the Erdős–Rényi network evolution chain is introduced as a subset of our model with the additional property of its stationary distribution matching the Erdős–Rényi random graph model. The stationary distributions of nodes and graphs are calculated for this subset alongside its entropy rate. The simulation results at the end of the article back up the proved theorems and calculated values.

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网络演化模型的信息论方法

引入了一种新的马尔可夫网络进化模型，并用信息论的方法对其进行了分析。证明了网络进化链模型是一个平稳的、遍历的随机过程。因此，可以将渐近均分性质应用于它。并对模型的熵率和典型序列进行了探讨。讨论了从网络中提取特定信息以及在连续时域内模拟网络演化的方法。此外，引入Erdős-Rényi网络进化链作为模型的子集，其平稳分布与Erdős-Rényi随机图模型相匹配。计算该子集的节点和图的平稳分布及其熵率。文章最后的仿真结果支持了所证明的定理和计算值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of complex networks MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.20

自引率

9.50%

发文量

期刊介绍： Journal of Complex Networks publishes original articles and reviews with a significant contribution to the analysis and understanding of complex networks and its applications in diverse fields. Complex networks are loosely defined as networks with nontrivial topology and dynamics, which appear as the skeletons of complex systems in the real-world. The journal covers everything from the basic mathematical, physical and computational principles needed for studying complex networks to their applications leading to predictive models in molecular, biological, ecological, informational, engineering, social, technological and other systems. It includes, but is not limited to, the following topics: - Mathematical and numerical analysis of networks - Network theory and computer sciences - Structural analysis of networks - Dynamics on networks - Physical models on networks - Networks and epidemiology - Social, socio-economic and political networks - Ecological networks - Technological and infrastructural networks - Brain and tissue networks - Biological and molecular networks - Spatial networks - Techno-social networks i.e. online social networks, social networking sites, social media - Other applications of networks - Evolving networks - Multilayer networks - Game theory on networks - Biomedicine related networks - Animal social networks - Climate networks - Cognitive, language and informational network