Clustering is a well-defined problem class in data mining, and many variations of it exists. However, practitioners often have additional constraints or quality scores that are not supported by standard algorithms. This has lead to the study of constrained clustering, which investigates generic methods to handle a variety of constraints and objectives. In our bioinformatics work, we were faced with exactly such a problem: a graph clustering problem with strict connectivity requirements and an objective function based on penalties rather than density of the clustering. In this paper, we explain the problem including the constraints and quality measures, and propose to use generic Mixed Integer Programming to solve it. We propose two approaches to handle the connectivity requirement in particular: one defined over all simple paths in the graph explicitly, and one based on cutting planes that enforce connectivity only when needed. Our experiments show that these approaches are able to solve the problem well. We hence demonstrate the applicability of generic OR methods on this application-driven data mining problem.