The structure and dynamics of higher-order networks.

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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.