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Statistical Properties of a Generalized Threshold Network Model

Author

Listed:
  • Yusuke Ide

    (Yokohama National University)

  • Norio Konno

    (Yokohama National University)

  • Naoki Masuda

    (The University of Tokyo)

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.

Suggested Citation

  • Yusuke Ide & Norio Konno & Naoki Masuda, 2010. "Statistical Properties of a Generalized Threshold Network Model," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 361-377, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9111-5
    DOI: 10.1007/s11009-008-9111-5
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    References listed on IDEAS

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    1. Christopher A. Najim & Ralph P. Russo, 2003. "On the Number of Subgraphs of a Specified Form Embedded in a Random Graph," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 23-33, March.
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    Cited by:

    1. Ide, Yusuke & Izuhara, Hirofumi & Machida, Takuya, 2016. "Turing instability in reaction–diffusion models on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 331-347.
    2. Chih-Sheng Hsieh & Michael D. König & Xiaodong Liu, 2012. "Network formation with local complements and global substitutes: the case of R&D networks," ECON - Working Papers 217, Department of Economics - University of Zurich, revised Feb 2017.

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