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

A. Fujihara, Masato Uchida, H. Miwa

Research output: Contribution to journalArticle

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1124-1130
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Issue number5
Publication statusPublished - 2010 Mar 1
Externally publishedYes



  • Complex networks
  • Extreme value theory
  • Power laws
  • Threshold network model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

Cite this