Abstract

In the analysis of complex networks, centrality measures and commu

nity structures play pivotal roles. For multilayer networks, a critical challenge

lies in effectively integrating information across diverse layers while accounting

for the dependence structures both within and between layers. We propose an

innovative two-stage regression model for multilayer networks, combining eigenvector centrality and network community structure within fourth-order tensor-

like multilayer networks. We develop new community-based centrality measures,

integrated into a regression framework. To address the inherent noise in network

data, we conduct separate analyses of centrality measures with and without measurement errors and establish consistency for the least squares estimates in the

regression model.

The proposed methodology is applied to the world inputoutput dataset, investigating how input-output network data among different

countries and industries influence the gross output of each industry.

Information

Preprint No.SS-2025-0101
Manuscript IDSS-2025-0101
Complete AuthorsZhuoye Han, Tiandong Wang, Zhiliang Ying
Corresponding AuthorsTiandong Wang
Emailstd_wang@fudan.edu.cn

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Acknowledgments

T. Wang gratefully acknowledges Science and Technology Commission of

Shanghai Municipality Grant 23JC1400700 and National Natural Science

Foundation of China Grant 12301660.

Both Z. Han and T. Wang also thank Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) for their financial support. This

research was partly funded by SIMIS under grant number SIMIS-ID-2024-

WE. They are grateful for the resources and facilities provided by SIMIS,

which were essential for the completion of this work.

Supplementary Materials

Section S1 provides technical proofs of main theorems, analyses under unknown community structure, and discussion of key assumptions. Section S2

presents additional simulation results, comparisons with alternative models,

and sensitivity analyses. Section S3 collects further details on the real-data

application using WIOD, including variable definitions, estimation results,

and comparisons of centrality measures.

Supplementary materials are available for download.