Methodology and Computing in Applied Probability

, Volume 12, Issue 3, pp 361–377 | Cite as

Statistical Properties of a Generalized Threshold Network Model

Article

Abstract

The threshold network model is a type of finite random graph. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of weights belong to given Borel sets. We extend several known limit theorems for the number of prescribed subgraphs and prove a uniform strong law of large numbers. We also prove two limit theorems for the local and global clustering coefficients.

Keywords

Complex networks Threshold network models Random graphs 

AMS 2000 Subject Classifications

05C80 60F15 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Applied MathematicsYokohama National UniversityYokohamaJapan
  2. 2.Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan

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