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.

翻译：核心-边缘检测旨在将复杂网络中的节点划分为两个子集：一个与整个网络紧密连接的核心，以及一个与核心紧密连接但内部连接稀疏的边缘。多路网络记录了同一组节点在不同层上的不同类型交互，在其中定义核心-边缘结构并非易事，因为一个节点可能在某些层属于核心，而在其他层属于边缘。当前最先进的方法依赖于各层度向量的线性组合，其层权重需要先验选择。我们提出了一种用于多路网络的非线性谱方法，通过最大化一个合适的非凸齐次目标函数，并采用交替不动点迭代，同时优化节点和层的核心度向量。我们证明了在可容许超参数选择下的全局最优性和收敛性保证，以及在其余情况下的局部最优收敛性。我们推导了一个定量度量，用于评估给定多路核心-边缘结构的质量，从而能够确定最优核心大小。在合成和真实网络上的数值实验表明，我们的方法对噪声层具有鲁棒性，并且在多种核心-边缘质量指标上优于基线方法。特别是，所有基于层聚合的方法在与新型优化的层核心度向量权重结合使用时都得到了改进。由于我们的方法运行时间与网络边数呈线性关系，因此它可扩展到大规模多路网络。