Mathematical foundations of the GraphBLAS

Jeremy Kepner, Peter Aaltonen, David Bader, Aydin Buluc, Franz Franchetti, John Gilbert, Dylan Hutchison, Manoj Kumar, Andrew Lumsdaine, Henning Meyerhenke, Scott Mcmillan, Carl Yang, John D. Owens, Marcin Zalewski, Timothy Mattson, Jose Moreira

Research output: Chapter in Book/Report/Conference proceedingConference contribution

165 Scopus citations


The GraphBLAS standard ( is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

Original languageEnglish (US)
Title of host publication2016 IEEE High Performance Extreme Computing Conference, HPEC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781509035250
StatePublished - Nov 28 2016
Externally publishedYes
Event2016 IEEE High Performance Extreme Computing Conference, HPEC 2016 - Waltham, United States
Duration: Sep 13 2016Sep 15 2016

Publication series

Name2016 IEEE High Performance Extreme Computing Conference, HPEC 2016


Conference2016 IEEE High Performance Extreme Computing Conference, HPEC 2016
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Hardware and Architecture
  • Computational Mathematics


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