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)

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.

Original languageEnglish
Pages (from-to)1124-1130
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume389
Issue number5
DOIs
Publication statusPublished - 2010 Mar 1
Externally publishedYes

Fingerprint

Extreme Value Theory
Threshold Model
Weight Function
Network Model
Theoretical Analysis
Power Law
Generalized Pareto Distribution
Weight Distribution
Clustering Coefficient
thresholds
Degree Distribution
Identically distributed
Range of data
Distribution Function
Random variable
Numerical Results
Prediction
random variables
Vertex of a graph
Theorem

Keywords

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

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

Cite this

Universal power laws in the threshold network model : A theoretical analysis based on extreme value theory. / Fujihara, A.; Uchida, Masato; Miwa, H.

In: Physica A: Statistical Mechanics and its Applications, Vol. 389, No. 5, 01.03.2010, p. 1124-1130.

Research output: Contribution to journalArticle

@article{ca5b8d20ef7b450794df9271e90e9ed4,
title = "Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory",
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, Extreme value theory, Power laws, Threshold network model",
author = "A. Fujihara and Masato Uchida and H. Miwa",
year = "2010",
month = "3",
day = "1",
doi = "10.1016/j.physa.2009.11.002",
language = "English",
volume = "389",
pages = "1124--1130",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "5",

}

TY - JOUR

T1 - Universal power laws in the threshold network model

T2 - A theoretical analysis based on extreme value theory

AU - Fujihara, A.

AU - Uchida, Masato

AU - Miwa, H.

PY - 2010/3/1

Y1 - 2010/3/1

N2 - 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.

AB - 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.

KW - Complex networks

KW - Extreme value theory

KW - Power laws

KW - Threshold network model

UR - http://www.scopus.com/inward/record.url?scp=71649115202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71649115202&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2009.11.002

DO - 10.1016/j.physa.2009.11.002

M3 - Article

VL - 389

SP - 1124

EP - 1130

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 5

ER -