Geometric fractal growth model for scale-free networks

被引：149

作者：

Jung, S. ^{[1
]}

Kim, S. ^{[1
]}

Kahng, B. ^{[2
]}

机构：

[1] Nonlinear and Complex Syst. Lab., Department of Physics, Pohang Univ. of Sci. and Technology, Pohang, Kyongbuk 790-784, Korea, Republic of

[2] School of Physics, Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea, Republic of

来源：

| 2002年 / American Physical Society卷 / 65期

关键词：

Fractals - Hierarchical systems - Large scale systems - Mathematical models - Poisson distribution - Probability distributions - Topology - Trees (mathematics);

D O I：

10.1103/PhysRevE.65.056101

中图分类号：

学科分类号：

摘要：

We introduce a deterministic model for scale-free networks, whose degree distribution follows a power law with the exponent y. At each time step, each vertex generates its offspring, whose number is proportional to the degree of that vertex with proportionality constant m-1 (m>1). We consider the two cases: First, each offspring is connected to its parent vertex only, forming a tree structure. Second, it is connected to both its parent and grandparent vertices, forming a loop structure, We find that both models exhibit power-law behaviors in their degree distributions with the exponent γ=1+ln(2m-1)/ lnw. Thus, by tuning m, the degree exponent can be adjusted in the range, 2<γy<3. We also solve analytically a mean shortest-path distance d between two vertices for the tree structure, showing the small-world behavior, that is, d∼ln N/ln k¯, where N is system size, and k¯ is the mean degree. Finally, we consider the case that the number of offspring is the same for all vertices, and find that the degree distribution exhibits an exponential-decay behavior. © 2002 The American Physical Society.

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