<s>
In	O
structure	B-Algorithm
mining	I-Algorithm
,	O
a	O
graph	B-Algorithm
kernel	I-Algorithm
is	O
a	O
kernel	O
function	O
that	O
computes	O
an	O
inner	O
product	O
on	O
graphs	B-Application
.	O
</s>
<s>
Graph	B-Algorithm
kernels	I-Algorithm
can	O
be	O
intuitively	O
understood	O
as	O
functions	O
measuring	O
the	O
similarity	O
of	O
pairs	O
of	O
graphs	B-Application
.	O
</s>
<s>
They	O
allow	O
kernelized	O
learning	O
algorithms	O
such	O
as	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
to	O
work	O
directly	O
on	O
graphs	B-Application
,	O
without	O
having	O
to	O
do	O
feature	B-Algorithm
extraction	I-Algorithm
to	O
transform	O
them	O
to	O
fixed-length	O
,	O
real-valued	O
feature	B-Algorithm
vectors	I-Algorithm
.	O
</s>
<s>
Concepts	O
of	O
graph	B-Algorithm
kernels	I-Algorithm
have	O
been	O
around	O
since	O
the	O
1999	O
,	O
when	O
D	O
.	O
Haussler	O
introduced	O
convolutional	O
kernels	O
on	O
discrete	O
structures	O
.	O
</s>
<s>
as	O
kernels	O
on	O
graphs	B-Application
,	O
i.e.	O
</s>
<s>
defined	O
kernels	O
between	O
graphs	B-Application
.	O
</s>
<s>
described	O
the	O
history	O
of	O
graph	B-Algorithm
kernels	I-Algorithm
and	O
their	O
evolution	O
over	O
two	O
decades	O
.	O
</s>
<s>
The	O
marginalized	O
graph	B-Algorithm
kernel	I-Algorithm
has	O
been	O
shown	O
to	O
allow	O
accurate	O
predictions	O
of	O
the	O
atomization	O
energy	O
of	O
small	O
organic	O
molecules	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
kernel	O
between	O
graphs	B-Application
is	O
the	O
random	O
walk	O
kernel	O
,	O
which	O
conceptually	O
performs	O
random	O
walks	O
on	O
two	O
graphs	B-Application
simultaneously	O
,	O
then	O
counts	O
the	O
number	O
of	O
paths	O
that	O
were	O
produced	O
by	O
both	O
walks	O
.	O
</s>
<s>
This	O
is	O
equivalent	O
to	O
doing	O
random	O
walks	O
on	O
the	O
direct	O
product	O
of	O
the	O
pair	O
of	O
graphs	B-Application
,	O
and	O
from	O
this	O
,	O
a	O
kernel	O
can	O
be	O
derived	O
that	O
can	O
be	O
efficiently	O
computed	O
.	O
</s>
<s>
Another	O
examples	O
is	O
the	O
Weisfeiler-Lehman	O
graph	B-Algorithm
kernel	I-Algorithm
which	O
computes	O
multiple	O
rounds	O
of	O
the	O
Weisfeiler-Lehman	O
algorithm	O
and	O
then	O
computes	O
the	O
similarity	O
of	O
two	O
graphs	B-Application
as	O
the	O
inner	O
product	O
of	O
the	O
histogram	O
vectors	O
of	O
both	O
graphs	B-Application
.	O
</s>
<s>
By	O
restricting	O
to	O
the	O
colors	O
that	O
occur	O
in	O
both	O
graphs	B-Application
,	O
the	O
computation	O
is	O
still	O
feasible	O
.	O
</s>
