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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