Optimality in group-driven social dynamics on hypergraphs

TL;DR

This paper investigates how hypergraph structural properties influence social dynamics, revealing optimal levels of nestedness and social reinforcement for contagion and consensus processes.

Contribution

It introduces the facet-based approximate master equation method and analyzes the impact of hyperedge nestedness and social reinforcement on social dynamics.

Findings

Hyperedge nestedness causes non-monotonic changes in contagion thresholds.

Consensus time scales as A ln N, with optimal social reinforcement at intermediate levels.

Higher-order interactions critically shape the efficiency of social processes.

Abstract

We explore the role of intrinsic structural properties of hypergraphs in governing group-driven social dynamics with social reinforcement. First, we analyze simplicial contagion dynamics on random hypergraphs in which the level of hyperedge nestedness is systematically controlled. By developing the facet-based approximate master equation (FAME) method, we demonstrate that hyperedge nestedness induces a non-monotonic change in the outbreak threshold for simplicial contagion, displaying the lowest threshold at an intermediate level of hyperedge nestedness due to competition between simple and higher-order contagion processes. Next, we formulate the group-driven voter model (GVM) and investigate the consensus time for the GVM on hypergraphs with N nodes. Focusing on a representative case of the GVM, we show that the consensus time scales logarithmically with the system size as A ln N, where the prefactor A displays the fastest consensus formation at an intermediate level of social reinforcement due to competition between group-constraint and nonlinearity factors. Taken together, our results highlight the importance of competing effects arising from higher-order interactions in shaping optimality in group-driven social dynamical processes.