# Common adversaries form alliances: modelling complex networks via anti-transitivity

## TL;DR

This paper introduces an evolutionary model called ILAT that captures anti-transitivity in complex networks, explaining how enemies of enemies tend to become allies, and analyzes its structural properties.

## Contribution

The paper presents the ILAT model for anti-transitivity in networks, analyzing its dynamics and properties, which is a novel approach to modeling adversarial relationships.

## Key findings

- Generated networks exhibit densification and short path lengths.
- Graphs have bounded spectral expansion.
- Determined cop and domination numbers for ILAT graphs.

## Abstract

Anti-transitivity captures the notion that enemies of enemies are friends, and arises naturally in the study of adversaries in social networks and in the study of conflicting nation states or organizations. We present a simplified, evolutionary model for anti-transitivity influencing link formation in complex networks, and analyze the model's network dynamics. The Iterated Local Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step, and joins anti-clones to the parent node's non-neighbor set. The graphs generated by ILAT exhibit familiar properties of complex networks such as densification, short distances (bounded by absolute constants), and bad spectral expansion. We determine the cop and domination number for graphs generated by ILAT, and finish with an analysis of their clustering coefficients. We interpret these results within the context of real-world complex networks and present open problems.