Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-01-21
Chaos 17, 026116 (2007)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 11 figures, a proceedings of the conference, "Optimization in complex networks." held in Los Alamos
Scientific paper
10.1063/1.2737827
A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box, and thereby, vertices in preassigned boxes can divide subsequent boxes into more than one pieces, 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 and thereby, vertices can belong to more than one box. Then, the number of distinct boxes a vertex belongs to is distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.
Goh Kwang-Il
Kahng Byungnam
Kim Dongseok
Kim Jinyoung Serena
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