Statistical Properties of a Generalized Threshold Network Model

Yusuke Ide; Norio Konno; Naoki Masuda

doi:10.1007/s11009-008-9111-5

Methodology and Computing in Applied Probability

September 2010, Volume 12, Issue 3, pp 361–377

Statistical Properties of a Generalized Threshold Network Model

Authors
Authors and affiliations

Yusuke IdeEmail author
Norio Konno
Naoki Masuda

Article

First Online:: 12 November 2008

Received:: 11 July 2007
Revised:: 19 October 2008
Accepted:: 24 October 2008

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

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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Authors and Affiliations

Yusuke Ide
- 1
Email author
Norio Konno
- 1
Naoki Masuda
- 2

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

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Statistical Properties of a Generalized Threshold Network Model

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