Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

TL;DR

This paper investigates a network model based on thresholding vertex weights, demonstrating it can produce realistic features like power-law degree distributions, clustering, and short paths, offering insights into the structure of complex networks.

Contribution

It introduces a threshold graph model with intrinsic vertex weights that naturally generates realistic complex network properties, differing from growth models.

Findings

Produces power-law degree distributions with stable exponent 2

Generates realistic clustering and short path lengths

Highlights differences from preferential attachment models

Abstract

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Caldarelli et al. (2002). Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.