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Ghim, Cheol-Min
Physical Biology & Biological Physics
Research Interests
  • Control of complex networks, Stochastic fluctuations in a cell, Biochemical information processing, Human microbiome, Ecological inference, Nonequilibrium active system

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Classes of the Shortest Pathway Structures in Scale Free Networks

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Title
Classes of the Shortest Pathway Structures in Scale Free Networks
Author
Goh, Kwang-IlOh, EulsikGhim, Cheol-MinKahng, ByungnamKim, Doochul
Issue Date
2004-08
Publisher
Springer
Citation
Lecture Notes in Physics, v.650, pp.105 - 125
Abstract
We study a problem of data packet transport between a pair of vertices on scale-free network, and introduce load of a vertex as the accumulated sum of a fraction of data packets traveling along the shortest pathways between every pair of vertices. It is found that the load distributions for many real-world networks follow a power law with an exponent which is close to either 2.2(1) (class I) or 2.0 (class II), insensitive to different values of the degree exponent in the range, 2 < < 3. The classification of scale-free networks into the two classes may stem from the characteristics of the shortest pathways structures. While the shortest pathways between a pair of vertices are multiply connected in the class I, they are almost singly connected in the class II. Such distinct topological features of the shortest pathways produce different behaviors in diverse problems such as the distribution of diameter change by the removal of a single vertex. Finally, we remark that since the two numerical values of the load exponent are too close, it still remains an open question if they are really robust. Analytic solution resolving this controversial issue is needed.
URI
https://scholarworks.unist.ac.kr/handle/201301/7098
URL
https://link.springer.com/chapter/10.1007%2F978-3-540-44485-5_5
DOI
10.1007/978-3-540-44485-5_5
ISSN
0075-8450
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PHY_Journal Papers
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