With its increasing popularity and reach, Twitter has recently become an interesting and promising database for social sciences. As a platform which is also used for political interactions, it offers a variety of research opportunities especially for political scientists. For this case study, we applied techniques of social network analysis to investigate Twitter communication networks in the context of international agreements. We visualized and analyzed network data to identify central actors and to make assumptions about the formation of the network. In this case, we describe the research process from data acquisition over data preparation to data analysis. Our aim is to enable other researchers interested in Twitter research to utilize Twitter data with a network analytical approach.