We investigate a variant of the many-to-many (hub) location-routing problem, which consists in partitioning the set of vertices of a graph into cycles containing exactly one hub each, and determining an extra cycle interconnecting all hubs. A local search heuristic that considers add/remove and swap operations is developed.Also, a branch-and-cut approach that solves an integer formulation is investigated.Computational experiments on several instances adapted from literature show that our algorithms are good to deal with small to medium-sized instances.