Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, SP, 13566-590, Brazil.
Dipartimento di Ingegneria Elettrica, Elettronica e Informatica, University of Catania, Catania, 95125, Italy.
Sci Rep. 2019 Feb 27;9(1):2866. doi: 10.1038/s41598-019-39340-w.
Nestedness has traditionally been used to detect assembly patterns in meta-communities and networks of interacting species. Attempts have also been made to uncover nested structures in international trade, typically represented as bipartite networks in which connections can be established between countries (exporters or importers) and industries. A bipartite representation of trade, however, inevitably neglects transactions between industries. To fully capture the organization of the global value chain, we draw on the World Input-Output Database and construct a multi-layer network in which the nodes are the countries, the layers are the industries, and links can be established from sellers to buyers within and across industries. We define the buyers' and sellers' participation matrices in which the rows are the countries and the columns are all possible pairs of industries, and then compute nestedness based on buyers' and sellers' involvement in transactions between and within industries. Drawing on appropriate null models that preserve the countries' or layers' degree distributions in the original multi-layer network, we uncover variations of country- and transaction-based nestedness over time, and identify the countries and industries that most contributed to nestedness. We discuss the implications of our findings for the study of the international production network and other real-world systems.
嵌套结构传统上被用于检测元群落和相互作用物种网络中的组装模式。人们还试图揭示国际贸易中的嵌套结构，通常表示为二部网络，其中可以在国家（出口国或进口国）和行业之间建立联系。然而，贸易的二部表示不可避免地忽略了行业之间的交易。为了全面捕捉全球价值链的组织，我们借鉴了世界投入产出数据库，并构建了一个多层网络，其中节点是国家，层是行业，并且可以在行业内和跨行业之间从卖家到买家建立联系。我们定义了买家和卖家的参与矩阵，其中行是国家，列是所有可能的行业对，然后基于买家和卖家在行业内和行业间交易中的参与度来计算嵌套度。利用适当的保留原始多层网络中国家或层的度分布的零模型，我们揭示了随时间变化的基于国家和基于交易的嵌套度的变化，并确定了对嵌套度贡献最大的国家和行业。我们讨论了我们的研究结果对国际生产网络和其他真实系统研究的意义。
