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Research Article


ON INFERENCE FOR MODULARITY STATISTICS IN STRUCTURED NETWORKS

Anirban Mitraa Department of Statistics, University of Pittsburgh, Pittsburgh,
PAView further author information
,
Konasale Prasadb Department of Psychiatry, University of Pittsburgh, Pittsburgh,
PAView further author information
&
Joshua Capec Department of Statistics, University of Wisconsin–Madison, Madison,
WICorrespondencejrcape@wisc.edu
https://orcid.org/0000-0002-1471-1650View further author information
Received 23 Nov 2022, Accepted 16 Mar 2024, Published online: 13 May 2024
 * Cite this article
 * https://doi.org/10.1080/10618600.2024.2336147
 * CrossMark


 

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ABSTRACT

This article revisits the classical concept of network modularity and its
spectral relaxations used throughout graph data analysis. We formulate and study
several modularity statistic variants for which we establish asymptotic
distributional results in the large-network limit for networks exhibiting nodal
community structure. Our work facilitates testing for network differences and
can be used in conjunction with existing theoretical guarantees for stochastic
blockmodel random graphs. Our results are enabled by recent advances in the
study of low-rank truncations of large network adjacency matrices. We provide
confirmatory simulation studies and real data analysis pertaining to the network
neuroscience study of psychosis, specifically schizophrenia. Collectively, this
article contributes to the limited existing literature to date on statistical
inference for modularity-based network analysis. Supplemental materials for this
article are available online.

KEYWORDS:

 * Blockmodel
 * Latent structure
 * Modularity
 * Network
 * Random graph




ACKNOWLEDGMENTS

The authors thank Nicholas Theis and the entire CONCEPT lab for real data
expertise. This research uses data from the UK Biobank, a major biomedical
database, obtained from the U.K. Biobank Resource under application number 68923
(PI: Konasale Prasad).


DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).


ADDITIONAL INFORMATION


FUNDING

This research was supported in part by the University of Pittsburgh Center for
Research Computing through the resources provided. Specifically, this work used
the H2P cluster which is supported by NSF award number OAC-2117681. JC
gratefully acknowledges support from the University of Wisconsin–Madison, Office
of the Vice Chancellor for Research and Graduate Education, with funding from
the Wisconsin Alumni Research Foundation.





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