English

Complex hypergraphs

Physics and Society 2023-08-21 v3 Disordered Systems and Neural Networks Discrete Mathematics Social and Information Networks

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.

Keywords

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)