The Coronavirus (COVID-19) outbreak has become one of the biggest threats to the global economy and financial markets . This study aims to analyze the effects of COVID-19 on 56 global stock indices from October 15, 2019 to August 7, 2020 by using a complex network method . Furthermore, the change of the network structure is analyzed in depth by dividing the stock markets into developed, emerging and frontier markets . The findings reveal a structural change in the form of node changes, reduced connectivity and significant differences in the topological characteristics of the network, due to COVID-19 . A contagion effect is also identified in the network structure of emerging markets, with the nodes behaving synchronously . The findings also reveal substantial clustering and homogeneity in the world stock market network, based on geographic positioning . Besides, the number of positive correlations in the global stock indices increased during the outbreak . The stock markets of France and Germany seem to be the most relevant developed markets, while Taiwan and Slovenia have this relevance in emerging and frontier markets . The findings of this study help regulators and practitioners to design important strategies in the light of varying stock market dynamics during COVID-19.