Analysis of the relationships among global stock markets is crucial for international investors, regulators, and policymakers, particularly during a crisis. Complex network theory was applied to analyze the relationship between global stock markets during the Russia–Ukraine war. Daily data from 55 stock markets from 6 August 2021 to 23 September 2023 were retrieved and used to investigate the changes in global stock market networks. The sample period was divided into 22 subsamples, using a 100-day rolling window rolled forward a trading month, and then long-range correlations based on distance matrices were calculated. These distance matrices were utilized to construct stock market networks. Moreover, minimum spanning trees (MSTs) were extracted from these financial networks for analytical purposes. Based on topological and structural analysis, we identified important/central nodes, distinct communities, vulnerable/stable nodes, and changes thereof with the escalation of war. The empirical findings reveal that the Russia–Ukraine war impacted the global stock markets’ network. However, its intensity varied with changes in the region and the passage of time due to the level of stock market integration and stage of war escalation, respectively. Stock markets of France, Germany, Canada, and Austria remained the most centrally connected within communities; surprisingly, the USA’s stock market is not on this list.