Methodology and Computing in Applied Probability

, Volume 12, Issue 3, pp 361–377

Statistical Properties of a Generalized Threshold Network Model


DOI: 10.1007/s11009-008-9111-5

Cite this article as:
Ide, Y., Konno, N. & Masuda, N. Methodol Comput Appl Probab (2010) 12: 361. doi:10.1007/s11009-008-9111-5


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.


Complex networks Threshold network models Random graphs 

AMS 2000 Subject Classifications

05C80 60F15 

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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