Properties of the Graph Modularity Matrix and its Applications
Benjamin Quiring, USDOE National Nuclear Security Administration (NNSA), Panayot S. Vassilevski · 2019
We study the popular modularity matrix and respective functional 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. Some illustrative examples which include algebraic multigrid (AMG) coarsening that follows strong direction of anisotropy in finite element problems as well as comparative performance results of the studied algorithm are presented.