We apply the multiple Graphical Horseshoe (mGHS) introduced by [2] to infer the network structure of four subtypes of breast cancer. The proposed approach relies on a novel multivariate shrinkage prior based on the Horseshoe prior that borrows strength and shares sparsity patterns across groups, improving posterior edge selection when the precision matrices are similar. On the other hand, there is no loss of performance when the groups are independent. We empirically demonstrate that mGHS outperforms competing approaches through both simulations and the breast cancer applications. Finally, we show an alternative approach for posterior edge selection based on model cuts.