We propose an extension of the stochastic block model for clustering sparse networks with compositional edge weights and zero-valued entries. The model accounts for two types of zeros in the compositional vectors: those arising from unobserved interactions and those due to deterministic constraints that prevent certain connections. It is based on a mixture of Dirichlet distributions, with parameters describing the sending and receiving intensities between clusters. To enable efficient estimation, we develop a hybrid likelihood inference approach for simultaneous parameter estimation and cluster assignment. The model reveals latent group structure in compositional networks and is applied to the Erasmus student exchange network, where zeros result either from a lack of exchange activity or from restrictions on intra-country mobility. The analysis identifies clusters of universities with distinct mobility patterns and varying degrees of attractiveness as exchange destinations.