Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-11-19
Physics
Condensed Matter
Statistical Mechanics
14 pages, 2 figures; Accepted in Physica A
Scientific paper
10.1016/j.physa.2009.11.002
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.
Fujihara Akihiro
Miwa Hiroyoshi
Uchida M. M. M.
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