GraphBLAS Mathematical Opportunities: Parallel Hypersparse, Matrix Based Graph Streaming, and Complex-Index Matrices

Hayden Jananthan; Jeremy Kepner; Michael Jones; Vijay Gadepally; Michael Houle; Peter Michaleas; Chasen Milner; Alex Pentland

GraphBLAS Mathematical Opportunities: Parallel Hypersparse, Matrix Based Graph Streaming, and Complex-Index Matrices

Data Structures and Algorithms 2025-09-24 v1

Authors: Hayden Jananthan , Jeremy Kepner , Michael Jones , Vijay Gadepally , Michael Houle , Peter Michaleas , Chasen Milner , Alex Pentland

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Abstract

The GraphBLAS high performance library standard has yielded capabilities beyond enabling graph algorithms to be readily expressed in the language of linear algebra. These GraphBLAS capabilities enable new performant ways of thinking about algorithms that include leveraging hypersparse matrices for parallel computation, matrix-based graph streaming, and complex-index matrices. Formalizing these concepts mathematically provides additional opportunities to apply GraphBLAS to new areas. This paper formally develops parallel hypersparse matrices, matrix-based graph streaming, and complex-index matrices and illustrates these concepts with various examples to demonstrate their potential merits.

Keywords

graph generation parallel algorithm data stream processing

Cite

@article{arxiv.2509.18984,
  title  = {GraphBLAS Mathematical Opportunities: Parallel Hypersparse, Matrix Based Graph Streaming, and Complex-Index Matrices},
  author = {Hayden Jananthan and Jeremy Kepner and Michael Jones and Vijay Gadepally and Michael Houle and Peter Michaleas and Chasen Milner and Alex Pentland},
  journal= {arXiv preprint arXiv:2509.18984},
  year   = {2025}
}

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HPEC 2025

GraphBLAS Mathematical Opportunities: Parallel Hypersparse, Matrix Based Graph Streaming, and Complex-Index Matrices

Abstract

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