The Iterated Local Transitivity Model for Tournaments

TL;DR

The paper introduces the ILTT model, a new method for generating dense, transitive tournaments that mimic real-world network properties, and analyzes its structural and spectral characteristics.

Contribution

It proposes the ILTT model based on transitivity for dense networks and explores its graph-theoretic properties and motifs.

Findings

Generated tournaments have small average distances.

Analyzed Hamilton cycles, spectral properties, and domination numbers.

Identified open problems and future directions.

Abstract

A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. We propose a new model for highly dense complex networks based on transitivity, called the Iterated Local Transitivity Tournament (or ILTT) model. In ILTT and a dual version of the model, we iteratively apply the principle of transitivity to form new tournaments. The resulting models generate tournaments with small average distances as observed in real-world complex networks. We explore properties of small subtournaments or motifs in the ILTT model and study its graph-theoretic properties, such as Hamilton cycles, spectral properties, and domination numbers. We finish with a set of open problems and the next steps for the ILTT model.