mathematics Article Global Value Chains of COVID-19 Materials: A Weighted Directed Network Analysis Georgios Angelidis 1 , Charalambos Bratsas 2 , Georgios Makris 2 , Evangelos Ioannidis 1,3 , Nikos C. Varsakelis 1 and Ioannis E. Antoniou 2, *   Citation: Angelidis, G.; Bratsas, C.; Makris, G.; Ioannidis, E.; Varsakelis, N.C.; Antoniou, I.E. Global Value Chains of COVID-19 Materials: A Weighted Directed Network Analysis. Mathematics 2021, 9, 3202. https:// doi.org/10.3390/math9243202 Academic Editors: Gaogao Dong and Jianguo Liu Received: 21 November 2021 Accepted: 9 December 2021 Published: 11 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 School of Economics, Faculty of Economic and Political Sciences, Complex Systems Analysis Laboratory (COSAL), Laboratory of Economic Analysis and Policy (LEAP), Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece; angelidig@econ.auth.gr (G.A.); ioannidek@math.auth.gr (E.I.); barsak@econ.auth.gr (N.C.V.) 2 School of Mathematics, Faculty of Sciences, Complex Systems Analysis Laboratory (COSAL), Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece; cbratsas@math.auth.gr (C.B.); geomak@auth.gr (G.M.) 3 School of Mathematics, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece * Correspondence: iantonio@math.auth.gr; Tel.: +30-2310-997-971 or +30-6937-222-337 Abstract: The COVID-19 pandemic caused a boom in demand for personal protective equipment, or so-called “COVID-19 goods”, around the world. We investigate three key sectoral global value chain networks, namely, “chemicals”, “rubber and plastics”, and “textiles”, involved in the production of these goods. First, we identify the countries that export a higher value added share than import, resulting in a “value added surplus”. Then, we assess their value added flow diversification using entropy. Finally, we analyze their egonets in order to identify their key affiliates. The relevant networks were constructed from the World Input-Output Database. The empirical results reveal that the USA had the highest surplus in “chemicals”, Japan in “rubber and plastics”, and China in “textiles”. Concerning value added flows, the USA was highly diversified in “chemicals”, Germany in “rubber and plastics”, and Italy in “textiles”. From the analysis of egonets, we found that the USA was the key supplier in all sectoral networks under consideration. Our work provides meaningful conclusions about trade outperformance due to the fact of surplus, trade flow robustness due to the fact of diversification, and trade partnerships due to the egonets analysis. Keywords: global value chain; complex networks; weighted directed networks; COVID-19 goods; personal protective equipment; degree; entropy 1. Introduction COVID-19 has led to an unprecedented global health crisis [1]. Most countries seek to obtain personal protective equipment (PPE) or “COVID-19 goods” and, in turn, man- ufacturers seek to obtain relevant raw materials or “COVID-19 materials”[2]. This has caused a boom in demand for PPE around the world [3–6]. PPE includes surgical masks, P2/N95 respirators, gloves, goggles, glasses, face shields, gowns, and aprons [7]. The basic raw materials involved in the production of PPE are “chemicals”, “rubber and plastics”, and “textiles” [8]. The high demand for these materials has resulted in uncertainty about their future availability. At the same time, lockdowns impose trade limitations on the interconnectedness among countries [9]. These limitations reduce the connectivity of the corresponding sectoral global value chain (GVC) networks, or “COVID-19 GVC nets”. Although countries with higher exports than imports—“high surplus countries”—play a key role, we must examine how robust their role is in COVID-19 GVC nets. Countries with high trade diversification are more robust than countries with low trade diversification, as they can absorb disruptive changes more effectively. Moreover, we need to identify the key affiliates of high surplus countries for two reasons: (a) policymakers should know the Mathematics 2021, 9, 3202. https://doi.org/10.3390/math9243202 https://www.mdpi.com/journal/mathematics