On a Sandy Beach: The GraphBLAS

Mike's Notes

Alex found this. It might be useful. For future reference.

The original webpage has the links, and the graphic looks better.

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05/01/2026

The GraphBLAS

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GraphBlas: 5/01/2026

The GraphBLAS Forum is an open effort to define standard building blocks for graph algorithms in the language of linear algebra.

An example graph and adjacency matrix

We believe that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. We believe that it is critical to move quickly and define such a standard, thereby freeing up researchers to innovate and diversify at the level of higher level algorithms and graph analytics applications. This effort was inspired by the Basic Linear Algebra Subprograms (BLAS) of dense Linear Algebra, and hence our working name for this standard is “the GraphBLAS”.

A key insight behind this work is that when a graph is represented by a sparse incidence or adjacency matrix, sparse matrix-vector multiplication is a step of breadth first search. By generalizing the pair of scalar operations involved in the linear algebra computations to define a semiring, we can extend the range of these primitives to support a wide range of parallel graph algorithms.

More information

The GraphBLAS Wikipedia Page
The C reference implementation is SuiteSparse:GraphBLAS, which implements the version 2.1.0 (final) C API.
Our 2013 manifesto for this project can be found here.
The mathematical definition of the GraphBLAS can be found here.
Background information about graphs in the language of linear algebra can be found in the book: Graph Algorithms in the Language of Linear Algebra, edited by J. Kepner and J. Gilbert, SIAM, 2011.
The Mathematics of Big Data by J. Kepner and H. Jananthan is the first book to present the common mathematical foundations of big data analysis across a range of applications and technologies.
A straw man proposal for the GraphBLAS can be found here
Gabor Szarnyas maintains a list of GraphBLAS pointers with lots of tutorial material.

Application Program Interface (API)

Current versions

GraphBLAS C API, version 2.0.0 (November 15, 2021)
GraphBLAS C API, version 2.1.0 (December 22, 2023)

Legacy versions

Version 1.0 (provisional) of the C language API was released on May 29, 2017 at the GABB workshop here. Version 1.1.0 (provisional) released on November 14, 2017. Version 1.2.0 was released on May 18, 2018. Version 1.3.0 was released on September 25, 2019.

Projects developing implementations of the GraphBLAS

SuiteSparse GraphBLAS (Texas A&M)
IBM GraphBLAS
GraphBLAS Template Library, GBTL (CMU-SEI/Indiana/PNNL)
GraphBLAST (UC Davis and LBNL)
MPI/C++ Combinatorial BLAS (CombBLAS)
Java Graphulo
Matlab/Octave D4M
GraphPad (Intel)

Programming Language Interfaces to The GraphBLAS API

MATLAB (comes with SuiteSparse). MATLAB R2021a and later uses SuiteSparse:GraphBLAS v3.1 for C=A*B when A and B are sparse. Release Notes, under Performance.
forGraphBLASGo - Go binding for SuiteSparse:GraphBLAS
pygraphblas Python library
python-graphblas Python library
pggraphblas Postgres extension
Julia library