The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited information about the structure of the system. We propose to use hypergraphs to represent these systems by introducing the concept of the complex hyper-network. We define several structural measures for complex hyper-networks. These measures characterize hyper-network structures on the basis of node participation in different hyper-edges (groups) and sub-hypergraphs. We also define two clustering coefficients, one characterizing the transitivity in the hyper-network through the proportion of hyper-triangles to paths of length two and the other characterizing the formation of triples of mutually adjacent groups in the hyper-network. All of these characteristics are studied in two different hyper-networks; a scientific collaboration hyper-network and an ecological competence hyper-network.
Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs
Institute for Cross-disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所 IFISC (CSIC-UIB)）；Instituto de Cálculo, FCEN, Universidad de Buenos Aires and CONICET（布宜诺斯艾利斯大学物理与数学学院计算研究所及阿根廷国家科学研究委员会）
HIF: The hypergraph interchange format for higher-order networks
University of Buenos Aires（布宜诺斯艾利斯大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Virginia（弗吉尼亚大学）；University of Trento（特伦托大学）；Broad Institute（博德研究所）；SGH Warsaw School of Economics（华沙经济高等学院）
