The weighted random graph model

TL;DR

This paper introduces the weighted random graph (WRG) model, an extension of Erdős-Rényi graphs for weighted networks, providing analytical insights into their structure and phase transitions, and comparing them with real networks.

Contribution

The paper presents the WRG model as a weighted extension of Erdős-Rényi graphs, with analytical characterizations of its degree, weight, and percolation properties, and compares its behavior to real networks.

Findings

WRG has a geometric weight distribution.

Percolation behavior in WRG resembles real networks.

Clustering analysis distinguishes WRG from real networks.

Abstract

We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behavior similar to what observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.