Transformability reveals the interplay of dynamics across different network orders

TL;DR

This paper introduces a comprehensive framework to analyze how different network dynamics interact across various network orders, revealing systemic transformations and universal models for instability that apply to multiple dynamical processes.

Contribution

It presents a novel holistic analysis framework linking dynamics across different network orders and demonstrates its applicability to contagion and opinion dynamics.

Findings

Identifies factors explaining interplay between higher-order and pairwise network dynamics.

Uncovers a universal model governing system instability.

Validates the framework across contagion and opinion dynamics.

Abstract

Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic analysis framework that bridges the interplays between dynamics across networks of different orders, demonstrating that these processes are not independent but can undergo systematic transformations. Focusing on contagion dynamics, we identify and quantify dynamical and structural factors that explains the interplay between dynamics on higher-order and pairwise networks, uncovering a universal model for system instability governed by these factors. Furthermore, we validate the findings from contagion dynamics to opinion dynamics, highlighting its broader applicability across diverse dynamical processes. Our findings reveal the intrinsic coupling between diverse dynamical processes, providing fresh insights into the distinct role of complex dynamics governed by higher-order interactions.