The Iterated Local Model for tournaments

TL;DR

The paper introduces the Iterated Local Model Tournament (ILMT), a new transitivity-based model for dense complex networks that produces highly connected, small-diameter tournaments with properties similar to real-world networks.

Contribution

It presents the ILMT, a novel iterative model for generating dense tournaments based on transitivity, cloning, and arc orientation, with analysis of its structural properties and universality.

Findings

ILMT generates tournaments with small diameters and high connectivity.

Many parameter choices produce quasirandom tournament sequences.

The model's graph properties include bounds on cop number, domination number, and chromatic number.

Abstract

Transitivity is a central, generative principle in social and other complex networks, capturing the tendency for two nodes with a common neighbor to form a direct connection. We propose a new model for highly dense, complex networks based on transitivity, called the Iterated Local Model Tournament (ILMT). In ILMT, we iteratively apply transitivity to form new tournaments by cloning nodes and their adjacencies, and either preserving or reversing the orientation of existing arcs between clones. The resulting model generates tournaments with small diameters and high connectivity as observed in real-world complex networks. We analyze subtournaments or motifs in the ILMT model and their universality properties. For many parameter choices, the model generates sequences of quasirandom tournaments. We also study the graph-theoretic properties of ILMT tournaments, including their cop number, domination number, and chromatic number. We finish with a set of open problems and variants of the ILMT model for oriented graphs.