Complex hypergraphs
arXiv:2209.07331 · doi:10.1103/PhysRevE.107.024316
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.
arXiv comment8 pages, 3 figures, Phys Rev E (In press)
References in corpus (15)
- Statistical mechanics of complex networks
- The structure of scientific collaboration networks
- Network robustness and fragility: Percolation on random graphs
- Evolution of the social network of scientific collaborations
- How Popular is Your Paper? An Empirical Study of the Citation Distribution
- Diffusion dynamics on multiplex networks
- Mathematical Formulation of Multi-Layer Networks
- Simplicial models of social contagion
- Random hypergraphs and their applications
- Citation Networks in High Energy Physics
- Simplicial Activity Driven Model
- Higher-order percolation processes on multiplex hypergraphs
- Evolutionary game model of group choice dilemmas on hypergraphs
- Covering Problems and Core Percolations on Hypergraphs
- Dense Power-law Networks and Simplicial Complexes