A local geometry of hyperedges in hypergraphs, and its applications to social networks

TL;DR

This paper introduces a new local geometry for hyperedges in hypergraphs to better model higher order social relations and proposes a hypergraph-based nearest neighbors method for social network analysis.

Contribution

It presents a novel local geometry of hyperedges and a new hypergraph nearest neighbors methodology for analyzing complex social network data.

Findings

Enhanced modeling of higher order social relations

New hypergraph nearest neighbors method

Potential for improved social network analysis

Abstract

In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such social networks. In this paper, we introduce a new local geometry of hyperdges in hypergraphs which allows to capture higher order relations among data points. Furthermore based on this new geometry, we also introduce new methodology--the nearest neighbors method in hypergraphs--for analyzing datasets arising from sociology.