Modeling Transitivity in Complex Networks

TL;DR

This paper introduces a new model for complex networks that incorporates transitivity, achieving high clustering coefficients similar to real-world networks and providing analytical and empirical validation.

Contribution

The paper presents a novel transitivity-based model for scale-free networks with analytical bounds on clustering, closely matching real-world network properties.

Findings

Model achieves high clustering coefficient independent of network size

Theoretical analysis supports the model's properties

Empirical results show accurate simulation of real-world networks

Abstract

An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific class like bipartite graphs, ii) they do not give an analytical argument for the high clustering coefficient of the model, and iii) their clustering coefficient is still significantly lower than real-world networks. In this paper, we propose a new model for complex networks which is based on adding transitivity to scale-free models. We theoretically analyze the model and provide analytical arguments for its different properties. In particular, we calculate a lower bound on the clustering coefficient of the model which is independent of the network size, as seen in real-world networks. More than theoretical analysis, the main properties of the model are evaluated empirically and it is shown that the model can precisely simulate real-world networks from different domains with and different specifications.