Spectral techniques for measuring bipartivity and producing partitions

IF 2.2 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of complex networks Pub Date : 2023-06-23 DOI:10.1093/comnet/cnad026

Azhar Aleidan, P. Knight

引用次数: 0

Abstract

Complex networks can often exhibit a high degree of bipartivity. There are many well-known ways for testing this, and in this article, we give a systematic analysis of characterizations based on the spectra of the adjacency matrix and various graph Laplacians. We show that measures based on these characterizations can be drastically different results and leads us to distinguish between local and global loss of bipartivity. We test several methods for finding approximate bipartitions based on analysing eigenvectors and show that several alternatives seem to work well (and can work better than more complex methods) when augmented with local improvement.

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测量双分性和产生分区的光谱技术

复杂的网络常常表现出高度的双方性。有许多众所周知的方法来测试这一点，在本文中，我们给出了基于邻接矩阵谱和各种图拉普拉斯算子的表征的系统分析。我们表明，基于这些特征的措施可能会产生截然不同的结果，并导致我们区分局部和全球双方性损失。我们测试了几种基于分析特征向量来寻找近似双分区的方法，并表明当增加局部改进时，几种替代方法似乎工作得很好(并且可以比更复杂的方法更好)。

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