Multilevel Graph Embedding
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE‐AC52‐07NA27344.
Numerical Linear Algebra with Applications
The goal of the present paper is the design of embeddings of a general sparse graph into a set of points in "ℝ𝑑 " for appropriate d ≥ 2. The embeddings that we are looking at aim to keep vertices that are grouped in communities together and keep the rest apart. To achieve this property, we utilize coarsening that respects possible community structures of the given graph. We employ a hierarchical multilevel coarsening approach that identifies communities (strongly connected groups of vertices) at every level. The multilevel strategy allows any given (presumably expensive) graph embedding algorithm to be made into a more scalable (and faster) algorithm. We demonstrate the presented approach on a number of given embedding algorithms and large‐scale graphs and achieve speed‐up over the methods in a recent paper.
© 2020 John Wiley & Sons, Ltd.
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Quiring, B., & Vassilevski, P. S. (2020). Multilevel graph embedding. Numerical Linear Algebra with Applications. https://doi.org/10.1002/nla.2326