Role discovery in graphs is an emerging area that allows analysis of complex graphs in an intuitive way. In contrast to community discovery, which finds groups of highly connected nodes, the role discovery problem finds groups of nodes that share similar topological structure in the graph, and hence a common role or function such as being a broker or a periphery node. However, existing work so far is completely unsupervised, which is undesirable for a number of reasons. We provide an alternating least squares framework that allows convex constraints to be placed on the role discovery problem, which can provide useful supervision. In particular we explore supervision to enforce i) sparsity, ii) diversity, and iii) alternativeness in the roles. We illustrate the usefulness of this supervision on various data sets and applications.