Social Groups, Social Media, and Higher Dimensional Social Structures: A Simplicial Model of Social Aggregation for Computational Communication Research

Abstract

By building on classical communication network literature, we present a computational approach to modeling tightly bound groups and social aggregations as higher dimensional social structures. Using the mathematical theory of simplicial complexes, these groups can be represented by geometric spatial elements (or simplexes) and a social aggregation a collection of simplexes (i.e., a simplicial complex). We discuss the uniting conditions that define a tightly bound group as a higher-dimensional group, which can be mathematically treated as nodes in a network of social aggregation. We utilize Facebook as a particularly relevant example to demonstrate innovative ways researchers can tap into digital data, in addition to traditional self-reported data, to advance communication research using the simplicial model, although the approach is applicable to many questions not involving communication technology.

Keywords:

• Communication Networks
• Computational Simulation
• Higher-Dimensional Groups
• Mathematical Modeling
• Social Aggregation

Acknowledgments

The authors would like to thank Travis Bartosh, Arleen Bejerano, Fran Dickson, Bill Eadie, Susan Kung, the editor, and the two anonymous reviewers for their input and support of this project. An early version of this article was presented at the National Communication Association Conference in 2011.