A tensor formalism for multilayer network centrality measures using the Einstein product

Complex systems that consist of diverse kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein product to model this type of networks. Several centrality measures, that are well known for single-layer networks, are extended to multilayer networks using tensors and their properties are investigated. In particular, subgraph centrality based on the exponential and resolvent of a tensor are considered. Krylov subspace methods based on the tensor format are introduced for computing approximations of different measures for large multilayer networks.