Fractality and self-similarity in scale-free networks

J. S. Kim, K. L. Goh, B. Kahng, D. Kim

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

Fractal scaling and self-similar connectivity behaviour of scale-free (SF) networks are reviewed and investigated in diverse aspects. We first recall an algorithm of box-covering that is useful and easy to implement in SF networks, the so-called random sequential box-covering. Next, to understand the origin of the fractal scaling, fractal networks are viewed as comprising of a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a spanning tree specifically based on the edge-betweenness centrality or load. We show that the skeleton is a non-causal tree, either critical or supercritical. We also study the fractal scaling property of the k-core of a fractal network and find that as k increases, not only does the fractal dimension of the &-core change but also eventually the fractality no longer holds for large enough k. Finally, we study the self-similarity, manifested as the scale-invariance of the degree distribution under coarse-graining of vertices by the box-covering method. We obtain the condition for self-similarity, which turns out to be independent of the fractality, and find that some non-fractal networks are self-similar. Therefore, fractality and self-similarity are disparate notions in SF networks.

Original languageEnglish
Article number177
JournalNew Journal of Physics
Volume9
DOIs
Publication statusPublished - 2007 Jun 28

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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