Published In
Computational Methods in Applied Mathematics
Document Type
Pre-Print
Publication Date
3-26-2026
Subjects
Graphs, Multilevel algorithms, Graph modularity
Abstract
We study the popular modularity matrix and respective functional ([20]) used in connection with graph clustering and derive some properties useful when performing vertex aggregation of the associated graph. These properties are employed in the derivation of a multilevel parallel pairwise aggregation algorithm. Comparative performance results of the studied algorithm applied to graph clustering tested against the popular Louvain algorithm [4], [3] are presented. Some illustrative examples show that the resulting aggregates if used in an adaptive algebraic multigrid (AMG) are able to follow strong direction of anisotropy in finite element problems. 1.
Rights
© Copyright the author(s) 2026
DOI
10.1515/cmam-2025-0177
Persistent Identifier
https://archives.pdx.edu/ds/psu/44582
Citation Details
Published as: Quiring, B., & Vassilevski, P. S. (2026). Properties of the Graph Modularity Matrix and Its Applications. Computational Methods in Applied Mathematics.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: (2026). Properties of the Graph Modularity Matrix and Its Applications. Computational Methods in Applied Mathematics.