Centrality measures and community structures play a pivotal role in the analysis of complex networks. To effectively model the impact of the network on our variable of interest, it is crucial to integrate information from the multilayer network, including the interlayer correlations of network data. In this study, we introduce a two-stage regression model that leverages the eigenvector centrality and network community structure of fourth-order tensor-like multilayer networks. Initially, we utilize the eigenvector centrality of multilayer networks, a method that has found extensive application in prior research. Subsequently, we amalgamate the network community structure to construct the community component centrality and individual component centrality of nodes, which are then incorporated into the regression model. Furthermore, we establish the asymptotic properties of the least squares estimates of the regression model coefficients. Our proposed method is employed to analyze data from the European airport network and The World Input-Output Database (WIOD), demonstrating its practical applicability and effectiveness.

翻译：中心性度量和社区结构在复杂网络分析中起着关键作用。为有效建模网络对目标变量的影响，必须整合多层网络信息，包括网络数据的层间相关性。本研究提出一种两阶段回归模型，该模型利用四阶张量型多层网络的特征向量中心性和网络社区结构。首先，我们采用多层网络的特征向量中心性——该方法在先前研究中已得到广泛应用。随后，通过融合网络社区结构构建节点的社区分量中心性和个体分量中心性，并将其纳入回归模型。进一步地，我们建立了回归模型系数最小二乘估计量的渐近性质。本文提出的方法被应用于欧洲机场网络和世界投入产出数据库（WIOD）的数据分析，验证了其实用性与有效性。