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 on different layers is nontrivial since a node may belong to the core in some layers and to the periphery in others. We propose a nonlinear spectral method for multiplex networks that simultaneously optimises a node and a layer coreness vector by maximising a suitable nonconvex homogeneous objective function by a provably convergent alternating fixed point iteration. 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 significantly outperforms baseline methods while improving the latter with our novel optimised layer coreness 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-外围检测旨在将复杂网络的节点划分为两个子集：一个与整个网络密集连接的核心，以及一个与核心密集连接但内部稀疏连接的外围。在多层网络中，由于同一组节点在不同层上记录不同类型的交互，节点可能在某些层属于核心而在其他层属于外围，因此定义核心-外围结构并非易事。我们提出了一种适用于多层网络的非线性谱方法，该方法通过可证明收敛的交替定点迭代最大化一个合适的非凸齐次目标函数，同时优化节点核心度向量和层核心度向量。我们推导了一种用于评估给定多层核心-外围结构质量的定量度量，该度量允许确定最优核心规模。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，且显著优于基线方法，同时通过我们新颖的优化层核心度权重改进了后者。由于我们方法的运行时间与网络的边数呈线性关系，因此可扩展至大规模多层网络。