# Mathematical Foundations of the GraphBLAS

Source: [Mathematical Foundations of the GraphBLAS](<https://www.sota2.com/research/paper/68fa45481e209131ce9175ea>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:54:42.628Z

Authors: Jeremy Kepner, Peter Aaltonen, David Bader, Ayd{\\i}n Buluc, Franz Franchetti, John Gilbert, Dylan Hutchison, Manoj Kumar, Andrew Lumsdaine, Henning Meyerhenke, Scott McMillan, Jose Moreira, John D. Owens, Carl Yang, Marcin Zalewski, Timothy Mattson

Published: 2016-06-18T18:46:20.000Z

## Abstract

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS 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 mul- tiplication. 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 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Knowledge Graph Retrieval on PKG Hop 5](<https://www.sota2.com/research/sota/knowledge-graph-retrieval-on-pkg-hop-5.md>): Knowledge Graph Retrieval; PKG Hop 5; QT (ms): 415.43.

- [Knowledge Graph Retrieval on PKG Hop 1](<https://www.sota2.com/research/sota/knowledge-graph-retrieval-on-pkg-hop-1.md>): Knowledge Graph Retrieval; PKG Hop 1; Query Time (ms): 3.03.

- [Knowledge Graph Retrieval on PKG Hop 4](<https://www.sota2.com/research/sota/knowledge-graph-retrieval-on-pkg-hop-4.md>): Knowledge Graph Retrieval; PKG Hop 4; QT (ms): 528.07.

- [Knowledge Graph Retrieval on PKG Hop 3](<https://www.sota2.com/research/sota/knowledge-graph-retrieval-on-pkg-hop-3.md>): Knowledge Graph Retrieval; PKG Hop 3; Query Time (ms): 291.89.

- [Knowledge Graph Retrieval on PKG Hop 2](<https://www.sota2.com/research/sota/knowledge-graph-retrieval-on-pkg-hop-2.md>): Knowledge Graph Retrieval; PKG Hop 2; Query Time (ms): 43.64.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1606.05790>)

[PDF](<https://arxiv.org/pdf/1606.05790.pdf>)