The Erasmus Programme is one of the most well-known student exchange programmes in the world, with over 200,000 higher education students availing of its benefits each year. We explore the Erasmus exchange data, aiming to identify clustering structure in the mobility patterns of students between countries. A directed weighted network of country-to-country student exchanges is constructed, with edge weights representing the percentage of students travelling from one country to any other. These edge weights are compositional in nature, so they cannot be assumed independent. We propose an extension of the stochastic block model for clustering network data with compositional edge weights, and compare its performance to that of other models.