Complex hypergraphs

TL;DR

This paper introduces complex hypergraphs, a new combinatorial structure that unifies various models of complex systems, enabling analytical insights into their component sizes and phase transitions.

Contribution

The paper presents complex hypergraphs as a novel unifying framework combining hypergraphs, multilayer networks, and simplicial complexes, with a new vectorization technique for analysis.

Findings

Calculated component size statistics for chygraphs

Identified the transition to a giant component in chygraphs

Demonstrated analytical tractability of the new model

Abstract

Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce complex hypergraphs (chygraphs), bringing together concepts from hypergraphs, multi-layer networks, simplicial complexes and hyperstructures. To illustrate the applicability of this combinatorial structure I calculate the component sizes statistics and identify the transition to a giant component. To this end I introduce a vectorization technique that tackles the multi-level nature of chygraphs. I conclude that chygraphs are a unifying representation of complex systems allowing for analytical insight.