Partitioning Weighted Undirected Graph
Even a simple Internet search reveals numerous papers on graph clustering approaches and algorithms. This paper is most likely the best starting point, as it presents a rather comprehensive overview of the topic in terms of the problem as well as approaches, methods and algorithms for solutions. The rest you can find easily via online search. In regard to graph clustering visualization, I recommend you to check my relevant answer - I'm pretty sure that the tools I reference there are able to visualize graph clusters as well.