将分形网络转换为小世界网络的一种新的随机重布线方法

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-18 DOI:10.1142/s0218348x23500895

Jian-Hui Li, Zuguo Yu, V. Anh, JIN-LONG Liu, AN-QI Peng

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引用次数: 0

摘要

分形和小词性质是复杂网络的两个重要性质。本文提出了一种新的随机重布线方法，将分形网络转化为小世界网络。我们从理论上证明了该方法可以保留所有节点的度(即度分布)和网络的连通性。此外，我们还从理论上证明了我们的方法也保留了树图的树形结构。我们的方法可以将许多不同类型的分形网络转化为小世界网络，而这些网络的度分布和连通性保持不变，证明了小世界网络的普遍性。此外，该方法也适用于其他类型的复杂网络。本文提出的重布线方法可用于更广泛的网络分析应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A NEW RANDOM REWIRING METHOD TO TRANSFORM FRACTAL NETWORKS INTO SMALL-WORLD NETWORKS

The fractal and small-word properties are two important properties of complex networks. In this paper, we propose a new random rewiring method to transform fractal networks into small-world networks. We theoretically prove that the proposed method can retain the degree of all nodes (hence the degree distribution) and the connectivity of the network. Further, we also theoretically prove that our method also retains the tree structure of tree graphs. Our method can transform many different types of fractal networks into small-world networks while the degree distribution and connectivity of these networks remain unchanged, demonstrating the generality of small-world networks. In addition, the method also works for other types of complex networks. The rewiring method proposed in this paper can be used in a broader range of applications of network analysis.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.