Network Transitivity and Matrix Models

TL;DR

This paper develops a static matrix model to analyze transitivity in random networks, introducing new analytical techniques and simulations to better understand clustering phenomena.

Contribution

It presents a novel static matrix model incorporating transitivity, resolving previous confusions and applying new analytic methods for clustering analysis.

Findings

New matrix model for network transitivity

Analytic techniques for clustering in static models

Simulation results supporting the model

Abstract

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix model, where matrices are random, but their elements take values 0 and 1 only. Confusion present in some papers where earlier attempts to incorporate transitivity in a similar framework have been made is hopefully dissipated. Inspired by more conventional matrix models, new analytic techniques to develop a static model with non-trivial clustering are introduced. Computer simulations complete the analytic discussion.