### 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 language | English |
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Article number | 026116 |

Journal | Chaos |

Volume | 17 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Aug 2 |

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### ASJC Scopus subject areas

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

### Cite this

*Chaos*,

*17*(2), [026116]. https://doi.org/10.1063/1.2737827

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

Research output: Contribution to journal › Article

*Chaos*, vol. 17, no. 2, 026116. https://doi.org/10.1063/1.2737827

}

TY - JOUR

T1 - A box-covering algorithm for fractal scaling in scale-free networks

AU - Kim, J. S.

AU - Goh, Kwang-Il

AU - Kahng, B.

AU - Kim, D.

PY - 2007/8/2

Y1 - 2007/8/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34547354360&partnerID=8YFLogxK

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U2 - 10.1063/1.2737827

DO - 10.1063/1.2737827

M3 - Article

VL - 17

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 2

M1 - 026116

ER -