New indicators for capturing the balances and roles of nations in the global knowledge exchange system

• A set of indicators are developed to assess the balance of knowledge flows. • We distinguish local and global flows and account for self-citations. • We apply double-fractionalization to capture international co-authorships. • Our indicators enable direct comparison of knowledge exchange roles of nations. • Empirical data reveals the trend of globalization and interdependence. The assessments of national involvement in the global system for exchange of knowledge traditionally focus on each country’s active contribution in the form of scientific publications and their citation impact. The use of knowledge in the same exchange is neglected. In this study, we develop a set of indicators to measure the balance of knowledge flows by recognizing citations as bidirectional relations between citing and cited publications, and thus between countries. The indicators distinguish between local and global knowledge flows, combine analyses with and without country self-citations, and incorporate a double-fractionalized method to cover the increasing phenomenon of international co-authorships. The indicators are both dependent and independent of size, thereby allowing for a direct country comparison of the balances and roles in knowledge exchange while at the same time identifying major actors. The indicators are presented with a thorough examination of their mathematical properties and their relations with each other. Data from Web of Science spanning 2000–2023 are used to exemplify how the balance indicators may identify the different roles of nations in the global exchange of knowledge. These roles may differ among areas of research and change over time. A general trend towards globalization and increasing interdependence is detected.