The structure and dynamics of higher-order networks.

本研究的主题是高阶相互作用的复杂网络的结构和动力学特性。具体地说，作为一种具有高阶交互作用的复杂网络，我们将超图作为研究对象，将聚类系数推广到超图上，超图是一种广泛应用的复杂网络结构特征的度量方法。我们称这种聚类系数为四次聚类系数。我们发现，四聚系数的分布在现实世界的超图是不同的超图配置模型中测量的系数的分布，作为一个空模型。然后，我们解析地导出了随机超图的聚类系数的平均值。接着，我们研究了各种超图结构模型的渗流性质，并与现实超图进行了比较。因此，在保持度-势相关的构型模型的情况下，我们确认了巨分支的分数与真实世界超图相似，并解析地导出了它的分数。

The topic of this research is the structural and dynamic characteristics of complex networks with higher-order interactions. Specifically, as a complex network with higher-order interactions, we deal with hypergraphs.We extend the clustering coefficient to hypergraph, which is widely used measure for the structural characteristics of complex networks. We call this clustering coefficient as quad clustering coefficient. We find that the distribution of quad clustering coefficients in real-world hypergraphs is different from the distribution of coefficients measured in the hypergraph configuration model, as a null model. Then, we derive analytically the average value of the clustering coefficient of the random hypergraphs.Next, we investigate the percolation properties of various hypergraph configuration models and compare them with real-world hypergraphs. As a result, in the case of the configuration model with preserved degree-cardinality correlation, we confirm that the fraction of the giant component is similar to the real-world hypergraphs, and we derive its fraction analytically.