<s>
GraphBLAS	B-Application
(	O
)	O
is	O
an	O
API	B-Application
specification	O
that	O
defines	O
standard	O
building	O
blocks	O
for	O
graph	O
algorithms	O
in	O
the	O
language	O
of	O
linear	B-Language
algebra	I-Language
.	O
</s>
<s>
GraphBLAS	B-Application
is	O
built	O
upon	O
the	O
notion	O
that	O
a	O
sparse	B-Algorithm
matrix	I-Algorithm
can	O
be	O
used	O
to	O
represent	O
graphs	O
as	O
either	O
an	O
adjacency	B-Algorithm
matrix	I-Algorithm
or	O
an	O
incidence	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
GraphBLAS	B-Application
specification	O
describes	O
how	O
graph	O
operations	O
(	O
e.g.	O
</s>
<s>
matrix	B-Architecture
multiplication	O
)	O
over	O
different	O
semirings	O
.	O
</s>
<s>
The	O
development	O
of	O
GraphBLAS	B-Application
and	O
its	O
various	O
implementations	O
is	O
an	O
ongoing	O
community	O
effort	O
,	O
including	O
representatives	O
from	O
industry	O
,	O
academia	O
,	O
and	O
government	O
research	O
labs	O
.	O
</s>
<s>
Graph	O
algorithms	O
have	O
long	O
taken	O
advantage	O
of	O
the	O
idea	O
that	O
a	O
graph	O
can	O
be	O
represented	O
as	O
a	O
matrix	B-Architecture
,	O
and	O
graph	O
operations	O
can	O
be	O
performed	O
as	O
linear	B-Architecture
transformations	I-Architecture
and	O
other	O
linear	O
algebraic	O
operations	O
on	O
sparse	B-Algorithm
matrices	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
matrix-vector	O
multiplication	O
can	O
be	O
used	O
to	O
perform	O
a	O
step	O
in	O
a	O
breadth-first	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
The	O
GraphBLAS	B-Application
specification	O
(	O
and	O
the	O
various	O
libraries	B-Library
that	O
implement	O
it	O
)	O
provides	O
data	B-General_Concept
structures	I-General_Concept
and	O
functions	O
to	O
compute	O
these	O
linear	O
algebraic	O
operations	O
.	O
</s>
<s>
In	O
particular	O
,	O
GraphBLAS	B-Application
specifies	O
sparse	B-Algorithm
matrix	I-Algorithm
objects	O
which	O
map	O
well	O
to	O
graphs	O
where	O
vertices	O
are	O
likely	O
connected	O
to	O
relatively	O
few	O
neighbors	O
(	O
i.e.	O
</s>
<s>
Originally	O
motivated	O
by	O
the	O
need	O
for	O
standardization	O
in	O
graph	O
analytics	O
,	O
similar	O
to	O
its	O
namesake	O
BLAS	B-Application
,	O
the	O
GraphBLAS	B-Application
standard	O
has	O
also	O
begun	O
to	O
interest	O
people	O
outside	O
the	O
graph	O
community	O
,	O
including	O
researchers	O
in	O
machine	O
learning	O
,	O
and	O
bioinformatics	O
.	O
</s>
<s>
GraphBLAS	B-Application
implementations	O
have	O
also	O
been	O
used	O
in	O
high-performance	O
graph	O
database	O
applications	O
such	O
as	O
Redis	B-Operating_System
.	O
</s>
<s>
The	O
GraphBLAS	B-Application
specification	O
has	O
been	O
in	O
development	O
since	O
2013	O
,	O
and	O
has	O
reached	O
version	O
2.0.0	O
as	O
of	O
November	O
2021	O
.	O
</s>
<s>
While	O
formally	O
a	O
specification	O
for	O
the	O
C	B-Language
programming	I-Language
language	I-Language
,	O
a	O
variety	O
of	O
programming	O
languages	O
have	O
been	O
used	O
to	O
develop	O
implementations	O
in	O
the	O
spirit	O
of	O
GraphBLAS	B-Application
,	O
including	O
C++	B-Language
,	O
Java	B-Language
,	O
and	O
Nvidia	B-Architecture
CUDA	I-Architecture
.	O
</s>
<s>
There	O
are	O
currently	O
two	O
fully-compliant	O
reference	O
implementations	O
of	O
the	O
GraphBLAS	B-Application
specification	O
.	O
</s>
<s>
Bindings	O
assuming	O
a	O
compliant	O
specification	O
exist	O
for	O
the	O
Python	B-Language
,	O
MATLAB	B-Language
,	O
and	O
Julia	B-Application
programming	I-Application
languages	I-Application
.	O
</s>
<s>
The	O
mathematical	O
foundations	O
of	O
GraphBLAS	B-Application
are	O
based	O
in	O
linear	B-Language
algebra	I-Language
and	O
the	O
duality	B-Algorithm
between	I-Algorithm
matrices	I-Algorithm
and	I-Algorithm
graphs	I-Algorithm
.	O
</s>
<s>
Each	O
graph	O
operation	O
in	O
GraphBLAS	B-Application
operates	O
on	O
a	O
semiring	O
,	O
which	O
is	O
made	O
up	O
of	O
the	O
following	O
elements	O
:	O
</s>
<s>
For	O
example	O
,	O
the	O
following	O
algebras	O
can	O
be	O
implemented	O
in	O
GraphBLAS	B-Application
:	O
</s>
<s>
While	O
the	O
GraphBLAS	B-Application
specification	O
generally	O
allows	O
significant	O
flexibility	O
in	O
implementation	O
,	O
some	O
functionality	O
and	O
implementation	O
details	O
are	O
explicitly	O
described	O
:	O
</s>
<s>
GraphBLAS	B-Application
objects	O
,	O
including	O
matrices	O
and	O
vectors	O
,	O
are	O
opaque	B-General_Concept
data	B-General_Concept
structures	I-General_Concept
.	O
</s>
<s>
Non-blocking	O
execution	O
mode	O
,	O
which	O
permits	O
lazy	O
or	O
asynchronous	B-Operating_System
evaluation	O
of	O
certain	O
operations	O
.	O
</s>
<s>
Masked	O
assignment	O
,	O
denoted	O
,	O
which	O
assigns	O
elements	O
of	O
matrix	B-Architecture
to	O
matrix	B-Architecture
only	O
in	O
positions	O
where	O
the	O
mask	O
matrix	B-Architecture
is	O
non-zero	O
.	O
</s>
<s>
The	O
GraphBLAS	B-Application
specification	O
also	O
prescribes	O
that	O
library	O
implementations	O
be	O
thread-safe	B-Operating_System
.	O
</s>
<s>
The	O
following	O
is	O
a	O
GraphBLAS	B-Application
2.0-compliant	O
example	O
of	O
a	O
breadth-first	B-Algorithm
search	I-Algorithm
in	O
the	O
C	B-Language
programming	I-Language
language	I-Language
.	O
</s>
