  In the analysis of complex networks, centrality measures and community
structures are two important aspects. For multilayer networks, one crucial task
is to integrate information across different layers, especially taking the
dependence structure within and between layers into consideration. In this
study, we introduce a novel two-stage regression model (CC-MNetR) that
leverages the eigenvector centrality and network community structure of
fourth-order tensor-like multilayer networks. In particular, we construct
community-based centrality measures, which are then incorporated into the
regression model. In addition, considering the noise of network data, we
analyze the centrality measure with and without measurement errors
respectively, and establish the consistent properties of the least squares
estimates in the regression. Our proposed method is then applied to the World
Input-Output Database (WIOD) dataset to explore how input-output network data
between different countries and different industries affect the Gross Output of
each industry.
