With the growth of Social Bookmark Services, such as Delicious, Digg or Hatena Bookmark, there is a large amount of data which can be expressed by tripartite network. Analyzing these tripartite networks is important, and community extraction is the method often used for this analysis. In this paper, we study the problems of extracting communities from tripartite networks based on modularity. Modularity is a measure to evaluate network partitioning, and there are several tripartite modularities proposed as the extension of Newman modularity. We identify the problems of these conventional tripartite modularities in network partitioning evaluation, especially when noisy edges are included in the network, and propose two new tripartite modularities that provide solutions to the problems. The results of the synthetic tripartite network experiments help us verify that our proposed methods evaluate network partitioning more effectively than the conventional ones. We also confirm meaningful community extraction results on a small real-world tripartite network. Furthermore, we propose a method for clustering edges as a means to explore network partitioning with large modularity values. It yields better community extraction results on synthetic tripartite network experiments compared with the method of clustering nodes directly.