Simplicial models of social aggregation I

TL;DR

This paper introduces a novel modeling approach for social aggregation using simplicial complexes, enabling richer representation of group interactions beyond traditional network models, with methods for simulation and analysis of social structures.

Contribution

It presents a new simplicial complex-based framework for modeling social aggregation, addressing limitations of network theory in representing higher-order group interactions.

Findings

Provides a mathematical foundation for simplicial social models

Develops a method to generate random simplicial complexes

Proposes measures to analyze social aggregation dynamics

Abstract

This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a node, and every social interaction is represented by a segment connecting two nodes. Early work in family interactions, as well as more recent work in the study of terrorist organizations, shows that network modeling may be insufficient to describe the complexity of human social structures. Specifically, network theory does not seem to have enough flexibility to represent higher order aggregations, where several agents interact as a group, rather than as a collection of pairs. The model we present here uses a well established mathematical theory, the theory of simplicial complexes, to address this complex issue prevalent in interpersonal and intergroup communication. The theory enables us to provide a richer graphical representation of social interactions, and to determine quantitative mechanisms to describe the robustness of a social structure. We also propose a methodology to create random simplicial complexes, with the purpose of providing a new method to simulate computationally the creation and disgregation of social structures. Finally, we propose several measures which could be taken and observed in order to describe and study an actual social aggregation occurring in interpersonal and intergroup contexts.