Consider a multilayer graph, where the different layers correspond to different proprietary social networks on the same ground set of users. Suppose that the owners of the different networks (called hosts) are mutually non-trusting parties: how can they compute a centrality score for each of the users using all the layers, but without disclosing information about their private graphs? Under this setting we study a suite of three centrality measures whose algebraic structure allows performing that computation with provable security and efficiency. The first measure counts the nodes reachable from a node within a given radius. The second measure extends the first one by counting the number of paths between any two nodes. The final one is a generalization to the multilayer graph case: not only the number of paths is counted, but also the multiplicity of these paths in the different layers is considered. We devise a suite of multiparty protocols to compute those centrality measures, which are all provably secure in the information-theoretic sense. One typical challenge and limitation of secure multiparty computation protocols is their scalability. We tackle this problem and devise a protocol which is highly scalable and still provably secure. We test our protocols on several real-world multilayer graphs: interestingly, the protocol to compute the most sensitive measure (i.e., the multilayer centrality) is also the most scalable one and can be efficiently run on very large networks.