Hypergraphs are generalizations of simple graphs that allow for the representation of complex group interactions beyond pairwise relationships. Clustering coefficients, which quantify the local link density in networks, have been widely studied even for hypergraphs. However, existing definitions of clustering coefficients for hypergraphs do not fully capture the pairwise relationships within hyperedges. In this study, we propose a novel clustering coefficient for hypergraphs that addresses this limitation by transforming the hypergraph into a weighted graph and calculating the clustering coefficient on the resulting graph. Our definition reflects the local link density more accurately than existing definitions. We demonstrate through theoretical evaluation on higher-order motifs that the proposed definition is consistent with the clustering coefficient for simple graphs and effectively captures relationships within hyperedges missed by existing definitions. Empirical evaluation on real-world hypergraph datasets shows that our definition exhibits similar overall clustering tendencies as existing definitions while providing more precise measurements, especially for hypergraphs with larger hyperedges. The proposed clustering coefficient has the potential to reveal structural characteristics in complex hypergraphs that are not detected by existing definitions, leading to a deeper understanding of the underlying interaction patterns in complex hypergraphs.

翻译：超图是简单图的推广，能够表示超越成对关系的复杂群体交互。聚类系数用于量化网络中的局部连接密度，即使在超图中也得到了广泛研究。然而，现有的超图聚类系数定义未能充分捕捉超边内的成对关系。在本研究中，我们提出了一种新颖的超图聚类系数，通过将超图转换为加权图并在所得图上计算聚类系数，以解决这一局限性。我们的定义比现有定义更准确地反映了局部连接密度。通过对高阶模体的理论评估，我们证明了所提出的定义与简单图的聚类系数具有一致性，并能有效捕捉现有定义所遗漏的超边内关系。在真实世界超图数据集上的实证评估表明，我们的定义展现出与现有定义相似的总体聚类趋势，同时提供了更精确的测量，尤其对于具有较大超边的超图。所提出的聚类系数有望揭示现有定义未能检测到的复杂超图中的结构特征，从而深化对复杂超图中潜在交互模式的理解。