Complex systems that consist of different kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein tensor 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 are introduced for computing approximations of different measures for large multilayer networks.

翻译：由不同类型实体以不同方式相互作用构成的复杂系统可通过多层网络建模。本文采用爱因斯坦张量积的张量形式体系对此类网络进行建模。将单层网络中若干经典中心性度量扩展至多层网络，并探究其张量性质。特别地，基于张量指数与预解式的子图中心性被纳入研究范畴。针对大规模多层网络，引入Krylov子空间方法以计算不同中心性度量的近似值。