Complex hypergraphs
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.
Cite
@article{arxiv.2209.07331,
title = {Complex hypergraphs},
author = {Alexei Vazquez},
journal= {arXiv preprint arXiv:2209.07331},
year = {2023}
}
Comments
8 pages, 3 figures, Phys Rev E (In press)