Rigorous results on the threshold network model

2005/05/31 by Norio Konno, Naoki Masuda, Rahul Roy +1 · 10 citations
Mathematics · Physics and Astronomy · #Central limit theorem #Complex Network Analysis Techniques #Convergence (economics) #Degree (music) #Enhanced Data Rates for GSM Evolution #Limit (mathematics) #Random Matrices and Applications #Random graph #Stochastic processes and statistical mechanics #Topology (electrical circuits) #Vertex (graph theory) #cond-mat.dis-nn #math.PR

paper · pdf · doi:10.1088/0305-4470/38/28/002

published in Journal of Physics A Mathematical and General 38(28), 6277-6291 (Institute of Physics) · 21 pages, Journal of Physics A, in press

arxiv created 2005/05/31 · openalex publication_date 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We analyse the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the vertex degree, degree correlation and the number of prescribed subgraphs. We also generalize some results in the spatially extended cases.

Citations

• Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights
• Geographical threshold graphs with small-world and scale-free properties
• Statistical mechanics of complex networks
• The Structure and Function of Complex Networks

Cited by

• Generalised thresholding of hidden variable network models with scale-free property