
\begin{abstract}
SuiteSparse:GraphBLAS is a full implementation of the GraphBLAS standard,
which defines a set of sparse matrix operations on an extended algebra of
semirings using an almost unlimited variety of operators and types.  When
applied to sparse adjacency matrices, these algebraic operations are equivalent
to computations on graphs.  GraphBLAS provides a powerful and expressive
framework for creating high-performance graph algorithms based on the elegant
mathematics of sparse matrix operations on a semiring.

When compared with MATLAB R2021a, some methods in GraphBLAS are up to
a million times faster than MATLAB, even when using the same syntax.
Typical speedups are in the range 2x to 30x.
The statement \verb'C(M)=A' when using MATLAB sparse matrices takes
$O(e^2)$ time where $e$ is the number of entries in \verb'C'.  GraphBLAS
can perform the same computation with the exact same syntax, but
in $O(e \log e)$ time (or $O(e)$ in some cases), and in practice that
means GraphBLAS can compute \verb'C(M)=A' for a large problem in under
a second, while MATLAB takes about 4 to 5 days.

SuiteSparse:GraphBLAS is under the Apache-2.0 license.
\end{abstract}

