A box-covering algorithm for fractal scaling in scale-free networks

J. S. Kim, Kwang-Il Goh, B. Kahng, D. Kim

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free (SF) networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box; thereby, vertices in preassigned boxes can divide subsequent boxes into more than one piece, but divided boxes are counted once. We find that such box-split allowance in the algorithm is a crucial ingredient necessary to obtain the fractal scaling for fractal networks; however, it is inessential for regular lattice and conventional fractal objects embedded in the Euclidean space. Next, the algorithm is viewed from the cluster-growing perspective that boxes are allowed to overlap; thereby, vertices can belong to more than one box. The number of distinct boxes a vertex belongs to is, then, distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.

Original languageEnglish
Article number026116
JournalChaos
Volume17
Issue number2
DOIs
Publication statusPublished - 2007 Aug 2

Fingerprint

Scale-free Networks
Complex networks
Fractals
boxes
Fractal
fractals
coverings
Covering
Scaling
scaling
apexes
Sequential Monte Carlo
Monte Carlo Algorithm
Fractal dimension
Fractal Dimension
Divides
Euclidean space
Overlap
Siméon Denis Poisson
Distinct

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A box-covering algorithm for fractal scaling in scale-free networks. / Kim, J. S.; Goh, Kwang-Il; Kahng, B.; Kim, D.

In: Chaos, Vol. 17, No. 2, 026116, 02.08.2007.

Research output: Contribution to journalArticle

Kim, J. S. ; Goh, Kwang-Il ; Kahng, B. ; Kim, D. / A box-covering algorithm for fractal scaling in scale-free networks. In: Chaos. 2007 ; Vol. 17, No. 2.
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