Multilayer Network Regression with Eigenvector Centrality and Community Structure

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.