2025-08-06 九州大学
赤い楕円（ハイパーエッジ）は「グループ的な関係性」を表しており、複数のノードが同時に関係し合う複雑な構造を可視化しています。従来の“1対1”のネットワークでは捉えきれない、現実に近いつながりを表現可能です。
＜関連情報＞
- https://www.kyushu-u.ac.jp/ja/researches/view/1301
- https://www.kyushu-u.ac.jp/f/62817/25_0806_01.pdf
- https://academic.oup.com/comnet/article-abstract/13/4/cnaf019/8221425?redirectedFrom=fulltext
ハイパーグラフのための統計的メソッド：パラメーター推定器、モデル選択、および比較検定 Statistical methods for hypergraphs: a parameter estimator, a model selection, and a comparative test
Grover E C Guzman , André Fujita
Journal of Complex Networks Published:02 August 2025
DOI:https://doi.org/10.1093/comnet/cnaf019
Abstract
Graphs have long been used to model complex systems, but real-world networks often exhibit fluctuations that challenge traditional graph-based methods. Random graph models and spectral techniques have been employed for statistical analysis. However, even these approaches are limited to dyadic relationships, whereas real-world systems often involve more complex interactions. Hypergraphs, which generalize graphs by allowing edges to connect multiple nodes, offer a more accurate representation of such complexity. Therefore, we propose a framework to statistically analyze real-world systems based on the hypergraph’s adjacency matrix spectrum. First, we introduce the Kullback–Leibler divergence to compare the spectra of two hypergraphs. We then develop statistical methods for hypergraph analysis, including a parameter estimator, a model selection approach, and a method to test whether two or more hypergraphs were generated by the same process (i.e. the same model and parameter set). Simulation experiments demonstrate the efficacy of our methods. Finally, we apply our approach to real-world hypergraphs as an illustrative example.
