Statistical Properties of a Generalized Threshold Network Model

  title={Statistical Properties of a Generalized Threshold Network Model},
  author={Y. Ide and N. Konno and N. Masuda},
  journal={Methodology and Computing in Applied Probability},
  • Y. Ide, N. Konno, N. Masuda
  • Published 2007
  • Mathematics
  • Methodology and Computing in Applied Probability
  • 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. 
    11 Citations
    Limit Theorems for the Average Distance and the Degree Distribution of the Threshold Network Model
    • Akihiro Fujihara, Yusuke Ide, +4 authors Masato Uchida
    • Mathematics
    • 2009
    • 9
    • PDF
    Scaling Laws for Connectivity in Random Threshold Graph Models with Non-Negative Fitness Variables
    • A. Makowski, O. Yağan
    • Mathematics, Computer Science
    • IEEE Journal on Selected Areas in Communications
    • 2013
    • 9
    • PDF
    Continuous-time quantum walks on the threshold network model
    • Y. Ide, N. Konno
    • Mathematics, Computer Science
    • Math. Struct. Comput. Sci.
    • 2010
    • 7
    • PDF
    Spectral Properties of the Threshold Network Model
    • 8
    • PDF
    Turing instability in reaction–diffusion models on complex networks
    • 10
    • PDF
    Generalised thresholding of hidden variable network models with scale-free property
    No . 109 Dynamic R & D Networks


    Rigorous results on the threshold network model
    • 12
    • PDF
    Class of correlated random networks with hidden variables.
    • 310
    • Highly Influential
    • PDF
    Designing threshold networks with given structural and dynamical properties.
    • 49
    • PDF
    Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights.
    • 36
    • PDF
    General formalism for inhomogeneous random graphs.
    • B. Söderberg
    • Medicine, Mathematics
    • Physical review. E, Statistical, nonlinear, and soft matter physics
    • 2002
    • 184
    • PDF
    Geographical threshold graphs with small-world and scale-free properties.
    • 78
    • PDF
    The Structure and Function of Complex Networks
    • M. Newman
    • Computer Science, Physics
    • SIAM Rev.
    • 2003
    • 10,665
    • PDF
    Vertex intrinsic fitness: how to produce arbitrary scale-free networks.
    • 104
    • PDF
    Scale-free networks from varying vertex intrinsic fitness.
    • 580
    • PDF
    Statistical mechanics of complex networks
    • 16,301
    • PDF