Acquaintance role for decision making and exchanges in social networks

TL;DR

This paper models social networks with multi-agent interactions using statistical mechanics, revealing that higher-order interactions significantly influence consensus formation at lower coupling strengths.

Contribution

It introduces a model for social networks with multi-agent interactions and analyzes how these interactions affect consensus dynamics using energy-entropy methods.

Findings

Higher-order interactions increase the importance of connectivity weights.

Consensus can be achieved at lower coupling strengths with larger interaction groups.

Connectivity plays a non-trivial role in social network dynamics.

Abstract

We model a social network by a random graph whose nodes represent agents and links between two of them stand for a reciprocal interaction; each agent is also associated to a binary variable which represents a dichotomic opinion or attribute. We consider both the case of pair-wise (p=2) and multiple (p>2) interactions among agents and we study the behavior of the resulting system by means of the energy-entropy scheme, typical of statistical mechanics methods. We show, analytically and numerically, that the connectivity of the social network plays a non-trivial role: while for pair-wise interactions (p=2) the connectivity weights linearly, when interactions involve contemporary a number of agents larger than two (p>2), its weight gets more and more important. As a result, when p is large, a full consensus within the system, can be reached at relatively small critical couplings with respect to the p=2 case usually analyzed, or, otherwise stated, relatively small coupling strengths among agents are sufficient to orient most of the system.