Cross-order induced behaviors in contagion dynamics on higher-order networks

2026-02-27

AI Summary

This study investigates how structural interdependencies in higher-order networks influence collective dynamics, with a focus on the misalignment between genuine higher-order mechanisms (HOMs) and observed higher-order behaviors (HOBs). By integrating information-theoretic measures—centered on synergy—with a simplicial complex-based SIS contagion model and higher-order structural analysis, the work uncovers a novel phenomenon termed “cross-order induced behavior”: significant behavioral signatures emerge at orders lacking direct mechanistic support. The authors demonstrate that this effect arises from neighboring-order mechanisms rather than inherent structural correlations. Furthermore, they establish synergy as a superior indicator for identifying the true mechanistic order, offering a new paradigm for efficiently pinpointing dominant higher-order drivers and thereby advancing the understanding of structure–dynamics relationships in complex higher-order systems.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Recent studies have shown that novel collective behaviors emerge in complex systems due to higher-order interactions. However, the way in which the structural correlations of these interactions shape such behaviors remains a significant gap in current research. To address this, we use signatures of higher-order behaviors (HOBs) to identify the underlying dynamical rules, or higher-order mechanisms (HOMs). In this work, we compare several HOB measures derived from information theory. Utilizing a simplicial SIS contagion model, we demonstrate that simpler, computationally efficient measures can serve as robust indicators of HOMs. We uncover the novel phenomenon of cross-order induced behaviors, where behavioral signatures emerge at interaction orders where no direct mechanism is present. Crucially, these cross-order HOBs are not simply induced by structural correlations -- such as nestedness and hyperedge overlap -- but they appear in the neighborhood of any HOM. Among the information-theoretic measures we tested, synergy is the most reliable indicator of the true order where the underlying mechanism is at play. These findings offer new insights into the relationship between the network structure and observed dynamics of higher-order systems.

Problem

• higher-order interactions
• contagion dynamics
• structural correlations
• cross-order behaviors
• collective behavior

Innovation

• higher-order interactions
• cross-order induced behaviors
• synergy
• simplicial contagion
• information-theoretic measures