Statistical properties of a generalized threshold network model

TL;DR

This paper introduces a generalized threshold network model, extending existing theories to analyze the statistical properties and convergence behaviors of complex random graphs with weighted vertices.

Contribution

It develops new limit theorems for subgraph counts and clustering coefficients in a generalized threshold network model, broadening the understanding of such networks.

Findings

Strong law of large numbers with uniform convergence

Limit theorems for local clustering coefficients

Limit theorems for global clustering coefficients

Abstract

The threshold network model is a type of finite random graphs. 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 to show that the strong law of large numbers can be uniform convergence. We also prove two limit theorems for the local and global clustering coefficients.