Many researchers have been studied visualization techniques to represent relationships between sets. However, most recent studies focused on the scalability of visualizing set relations, rather than on set-typed data itself. Although solving such problems is important, understanding the structural context of the entire data is also essential for analyzing data. We propose NetSet, which combines two techniques to resolve the limitations in representing set relationships. First, we construct a network to provide a structural overview of the set system. Then, we place a matrix layout to visualize intersections among sets. Finally, by combining these two techniques, NetSet enables them to complement each other. The combination gives analysts both the overview and specific views of the data. Furthermore, NetSet provides both flexible exploration of a set system and quantitative analysis of set intersections. We conducted a case study to demonstrate how the combination can be successfully applied to real data, namely topic-talks data from the TED organization.