Modelling community structure and temporal spreading on complex networks

Q1 Mathematics

Computational Social Networks Pub Date : 2020-03-09 DOI:10.21203/rs.3.rs-16363/v1

Vesa Kuikka

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引用次数: 6

Abstract

We present methods for analysing hierarchical and overlapping community structure and spreading phenomena on complex networks. Different models can be developed for describing static connectivity or dynamical processes on a network topology. In this study, classical network connectivity and influence spreading models are used as examples for network models. Analysis of results is based on a probability matrix describing interactions between all pairs of nodes in the network. One popular research area has been detecting communities and their structure in complex networks. The community detection method of this study is based on optimising a quality function calculated from the probability matrix. The same method is proposed for detecting underlying groups of nodes that are building blocks of different sub-communities in the network structure. We present different quantitative measures for comparing and ranking solutions of the community detection algorithm. These measures describe properties of sub-communities: strength of a community, probability of formation and robustness of composition. The main contribution of this study is proposing a common methodology for analysing network structure and dynamics on complex networks. We illustrate the community detection methods with two small network topologies. In the case of network spreading models, time development of spreading in the network can be studied. Two different temporal spreading distributions demonstrate the methods with three real-world social networks of different sizes. The Poisson distribution describes a random response time and the e-mail forwarding distribution describes a process of receiving and forwarding messages.

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复杂网络上群落结构和时间扩展的建模

我们提出了分析复杂网络中分层和重叠的群落结构和传播现象的方法。可以开发不同的模型来描述网络拓扑结构上的静态连接或动态过程。在本研究中，以经典的网络连通性和影响传播模型为例，建立了网络模型。结果的分析是基于描述网络中所有节点对之间相互作用的概率矩阵。一个热门的研究领域是在复杂网络中检测社区及其结构。本研究的社区检测方法是基于优化从概率矩阵计算的质量函数。提出了同样的方法来检测底层节点组，这些节点组是网络结构中不同子社区的构建块。我们提出了不同的量化度量来比较和排序社区检测算法的解。这些指标描述了子群落的性质:群落的强度、形成的概率和组成的稳健性。本研究的主要贡献是提出了一种分析复杂网络结构和动态的通用方法。我们用两个小的网络拓扑来说明社区检测方法。对于网络传播模型，可以研究网络中传播的时间发展。两种不同的时间分布证明了该方法在三个不同规模的现实社会网络中的应用。泊松分布描述了一个随机的响应时间，而电子邮件转发分布描述了一个接收和转发消息的过程。

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

Computational Social Networks Mathematics-Modeling and Simulation

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： Computational Social Networks showcases refereed papers dealing with all mathematical, computational and applied aspects of social computing. The objective of this journal is to advance and promote the theoretical foundation, mathematical aspects, and applications of social computing. Submissions are welcome which focus on common principles, algorithms and tools that govern network structures/topologies, network functionalities, security and privacy, network behaviors, information diffusions and influence, social recommendation systems which are applicable to all types of social networks and social media. Topics include (but are not limited to) the following: -Social network design and architecture -Mathematical modeling and analysis -Real-world complex networks -Information retrieval in social contexts, political analysts -Network structure analysis -Network dynamics optimization -Complex network robustness and vulnerability -Information diffusion models and analysis -Security and privacy -Searching in complex networks -Efficient algorithms -Network behaviors -Trust and reputation -Social Influence -Social Recommendation -Social media analysis -Big data analysis on online social networks This journal publishes rigorously refereed papers dealing with all mathematical, computational and applied aspects of social computing. The journal also includes reviews of appropriate books as special issues on hot topics.