Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory

A. Fujihara, M. Uchida and H. Miwa

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 5, 1124-1130

Abstract: We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a theoretical understanding of the distribution of independent and identically distributed random variables within a sufficiently high range. Specifically, the distribution could be generally expressed by a generalized Pareto distribution, which enabled us to formulate the generic weight distribution function. By using the theorem, we obtained the exact expressions of degree distribution and clustering coefficient which behaved as universal power laws within certain ranges of degrees. We also compared the theoretical predictions with numerical results and found that they were extremely consistent.

Keywords: Complex networks; Threshold network model; Extreme value theory; Power laws (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:5:p:1124-1130

DOI: 10.1016/j.physa.2009.11.002

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