A widespread perspective describes emotions as distinct categories bridged by fuzzy boundaries, indicating that emotions are distinct and dimensional at the same time. Theoretical and methodological approaches to this perspective still need further development. We conceptualize emotions as overlapping networks of causal relationships between emotion components—networks representing distinct emotions share components with and relate to each other. To investigate this conceptualization, we introduce network analysis to emotion research and apply it to the reanalysis of a data set on multiple positive emotions. Specifically, we describe the estimation of networks from data, and the detection of overlapping communities of nodes in these networks. The network perspective has implications for the understanding of distinct emotions, their co-occurrence, and their measurement.