World leaders have been increasingly using social media platforms as a tool for political communication. However, despite the growing research on governmental accounts on social media, virtually nothing is known about interactions among world leaders. Using a novel, cross-national dataset of Twitter communication for leaders of 193 countries for the period of 2012-2017, we construct retweet and mention networks to explore the patterns of leaders communication. We use social network analysis to conclude that the leaders interactions on social media closely resemble their interactions in the offline world. Besides, consistent with the democratic peace theory that underscores a special connection between democracies, we identify political regime as the main predictor of clustering between countries on Twitter. Finally, we explore the patterns of the leaders centrality to identify features that determine which leaders occupy more central positions in the network. Our findings yield new insights on how social media is used by government actors, and have important implications for our understanding of the impact of new technologies on the new forms of diplomacy.