Rigorous results on the threshold network model

Abstract

We analyze 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.

21 pages, Journal of Physics A, in press

References in corpus (7)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Class of correlated random networks with hidden variables
• A General Formalism for Inhomogeneous Random Graphs
• Subgraphs in random networks
• Geographical threshold graphs with small-world and scale-free properties
• Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Cited by in corpus (4)

• Infinite networks and variation of conductance functions in discrete Laplacians
• Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory
• Generalised thresholding of hidden variable network models with scale-free property
• Sequence Nets