## Abstract

In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential subgroups in hypergraphs, named (k,q)-core decomposition. The (k,q)-core is defined as the maximal subgraph in which each vertex has at least k hypergraph degrees and each hyperedge contains at least q vertices. The method contains a repeated pruning process until reaching the (k,q)-core, which shares similarities with a widely used k-core decomposition technique in a graph. Second, we analyze the pruning dynamics and the percolation transition with theoretical and numerical methods in random hypergraphs. We set up evolution equations for the pruning process, and self-consistency equations for the percolation properties. Based on our theory, we find that the pruning process generates a hybrid percolation transition for either k≥3 or q≥3. The critical exponents obtained theoretically are confirmed with finite-size scaling analysis. Next, when k=q=2, we obtain a unconventional degree-dependent critical relaxation dynamics analytically and numerically. Finally, we apply the (k,q)-core decomposition to a real coauthorship dataset and recognize the leading groups at an early stage.

Original language | English |
---|---|

Article number | 113645 |

Journal | Chaos, Solitons and Fractals |

Volume | 173 |

DOIs | |

Publication status | Published - 2023 Aug |

### Bibliographical note

Funding Information:This work was supported by the National Research Foundation of Korea with Grant No. NRF-2014R1A3A2069005 (B.K.), NRF-2019R1A 2C1003486 (D.-S.L.), NRF-2020R1A2C2003669 (K.-I.G.), KENTECH Research Grant No. KRG2021-01-007 at Korea Institute of Energy Technology (B.K.), and a KIAS Individual Grant No. CG079901 at Korea Institute for Advanced Study (D.-S.L.).

Publisher Copyright:

© 2023 Elsevier Ltd

## Keywords

- Critical dynamics
- Higher-order networks
- Hybrid phase transition
- Hypergraph
- Percolation

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics