Topological fractal networks introduced by mixed degree distribution

Liuhua Zou*, Wenjiang Pei, Tao Li, Zhenya He, Yiu Ming CHEUNG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

13 Citations (Scopus)


Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors. However, highly clustered scale-free network, with power-law degree distribution, or small-world network models, with exponential degree distribution, are not self-similarity. We investigate networks growth mechanism of the branching-deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors. It yields high clustering and spectrums of degree distribution ranging from algebraic to exponential, average shortest path length ranging from linear to logarithmic. We observe that the present networks fit well with small-world graphs and scale-free networks in both limit cases (exponential and algebraic degree distribution, respectively), obviously lacking self-similar property under a length-scale transformation. Interestingly, we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values. The results present a reliable connection among small-world graphs, scale-free networks and topological fractal networks, and promise a natural way to investigate universal origins of collective behaviors.

Original languageEnglish
Pages (from-to)592-600
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
Publication statusPublished - 1 Jul 2007

Scopus Subject Areas

  • Statistics and Probability
  • Condensed Matter Physics

User-Defined Keywords

  • Mixed scaling
  • Small-world networks
  • Topological fractal


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