Global value chains are formed through value-added trade, and some regions promote economic integration by concluding regional trade agreements to promote these chains. However, it has not been established to quantitatively assess the scope and extent of economic integration involving various sectors in multiple countries. In this study, we used the World Input–Output Database to create a cross-border sector-wise network of trade in value-added (international value-added network) covering the period of 2000–2014 and evaluated them using network science methods. By applying Infomap to the international value-added network, we confirmed two regional communities: Europe and the Pacific Rim. We applied Helmholtz–Hodge decomposition to the value-added flows within the region into potential and circular flows, and clarified the annual evolution of the potential and circular relationships between countries and sectors. The circular flow component of the decomposition was used to define an economic integration index. Findings confirmed that the degree of economic integration in Europe declined sharply after the economic crisis in 2009 to a level lower than that in the Pacific Rim. The European economic integration index recovered in 2011 but again fell below that of the Pacific Rim in 2013. Moreover, sectoral economic integration indices suggest what Europe depends on Russia in natural resources makes the European economic integration index unstable. On the other hand, the indices of the Pacific Rim suggest the steady economic integration index of the Pacific Rim captures the stable global value chains from natural resources to construction and manufactures of motor vehicles and high-tech products.

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In the original article, there was an error in affiliation 1. The correct affiliation appears above. Additionally, references [15] and [52] contained formatting errors. The correct versions are as follows: 15. Ikeda Y, Iyetomi H, Mizuno T. Big data analysis on global community formation and isolation. Springer (2021). 52. ASEAN. Declaration of ASEAN Concord II (Bali Concord II) (2003). Available from:https://asean.org/speechandstatement/declaration-of-asean-concord-ii-baliconcord-ii/ (Accessed 12, September 2022).The authors apologize for these errors and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

Economic integration is underway in East Asia and the Asia-Pacific region, including the Association of Southeast Asian Nations (ASEAN) community-building process, with the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP) coming into effect in 2018 and the Regional Comprehensive Economic Partnership (RCEP) in 2022. While these Regional Trade Agreements (RTAs) have deepened multilateral relations, there is an insufficient mechanism to quantify multilateral diplomacy within the region. Therefore, this study analyzed the region from three perspectives: countries that have contributed to diplomacy for intra-regional cooperation (diplomatic ranking), the cohesiveness of countries in diplomatic stances (diplomatic clusters), and the synchronization period of cooperative events (diplomatic synchronization); and we quantified them by the ranking of diplomatic centrality, blockmodeling of the signed network, and analytic signal, respectively. For analysis, we used bilateral event data to create a political distance network consisting of the original East Asia Summit (EAS) member countries (ASEAN+6) and the United States for the period 1985–2020 and to define diplomatic centrality. Diplomatic ranking indicated three major trends: 1985–1992, 1993–2011, and 2012–2020. Until 1992, Japan, the ASEAN member states (AMS), and Australia ranked at the top, and from 1993 to 2011, Japan and China almost dominated the top. Since 2012, AMS have joined Japan and China in the top ranks. Diplomatic clusters showed the stances of Australia and New Zealand were closest. Throughout the 36 years, the stances of Japan and Republic of Korea were also closer, followed by China, AMS, and the United States. Diplomatic synchronization quantified the progress of regionalism in East Asia. Furthermore, diplomatic rankings in synchronous periods revealed the difference between the diplomatic positions of Japan and China in East Asia and illustrated that AMS were at the center of multilateral diplomacy in the region in 2018–2019.