We set out a graphical model for describing probability distributions over labeled partitions of an undirected graph which are conditioned on observed data. We show how to efficiently perform exact inference in these models, by exploiting the structure of the graph and adapting the sum-product and max-product algorithms. The method can be used for partitioning and labeling hand-drawn ink fragments, image data, speech data and natural language data amongst other types of data elements. A significant performance increase is obtained by labeling and partitioning simultaneously. It is also possible to partition without labeling.