A nonlinear spectral core-periphery detection method for multiplex networks

Core-periphery detection aims to separate the nodes of a complex network into two subsets: a core that is densely connected to the entire network and a periphery that is densely connected to the core but sparsely connected internally. The definition of core-periphery structure in multiplex networks that record different types of interactions between the same set of nodes but on different layers is nontrivial since a node may belong to the core in some layers and to the periphery in others. The current state-of-the-art approach relies on linear combinations of individual layer degree vectors whose layer weights need to be chosen a-priori. We propose a nonlinear spectral method for multiplex networks that simultaneously optimizes a node and a layer coreness vector by maximizing a suitable nonconvex homogeneous objective function by an alternating fixed point iteration. We prove global optimality and convergence guarantees for admissible hyper-parameter choices and convergence to local optima for the remaining cases. We derive a quantitative measure for the quality of a given multiplex core-periphery structure that allows the determination of the optimal core size. Numerical experiments on synthetic and real-world networks illustrate that our approach is robust against noisy layers and outperforms baseline methods with respect to a variety of core-periphery quality measures. In particular, all methods based on layer aggregation are improved when used in combination with the novel optimized layer coreness vector weights. As the runtime of our method depends linearly on the number of edges of the network it is scalable to large-scale multiplex networks.