<s>
PageRank	B-Algorithm
(	O
PR	O
)	O
is	O
an	O
algorithm	O
used	O
by	O
Google	B-Application
Search	I-Application
to	O
rank	O
web	O
pages	O
in	O
their	O
search	B-Application
engine	I-Application
results	O
.	O
</s>
<s>
PageRank	B-Algorithm
is	O
a	O
way	O
of	O
measuring	O
the	O
importance	O
of	O
website	O
pages	O
.	O
</s>
<s>
According	O
to	O
Google	B-Application
:	O
Currently	O
,	O
PageRank	B-Algorithm
is	O
not	O
the	O
only	O
algorithm	O
used	O
by	O
Google	B-Application
to	O
order	O
search	B-Application
results	I-Application
,	O
but	O
it	O
is	O
the	O
first	O
algorithm	O
that	O
was	O
used	O
by	O
the	O
company	O
,	O
and	O
it	O
is	O
the	O
best	O
known	O
.	O
</s>
<s>
As	O
of	O
September	O
24	O
,	O
2019	O
,	O
PageRank	B-Algorithm
and	O
all	O
associated	O
patents	O
are	O
expired	O
.	O
</s>
<s>
PageRank	B-Algorithm
is	O
a	O
link	O
analysis	O
algorithm	O
and	O
it	O
assigns	O
a	O
numerical	O
weighting	B-General_Concept
to	O
each	O
element	O
of	O
a	O
hyperlinked	O
set	O
of	O
documents	O
,	O
such	O
as	O
the	O
World	O
Wide	O
Web	O
,	O
with	O
the	O
purpose	O
of	O
"	O
measuring	O
"	O
its	O
relative	O
importance	O
within	O
the	O
set	O
.	O
</s>
<s>
A	O
PageRank	B-Algorithm
results	O
from	O
a	O
mathematical	O
algorithm	O
based	O
on	O
the	O
webgraph	B-Application
,	O
created	O
by	O
all	O
World	O
Wide	O
Web	O
pages	O
as	O
nodes	O
and	O
hyperlinks	O
as	O
edges	O
,	O
taking	O
into	O
consideration	O
authority	O
hubs	O
such	O
as	O
cnn.com	O
or	O
mayoclinic.org	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
of	O
a	O
page	O
is	O
defined	O
recursively	O
and	O
depends	O
on	O
the	O
number	O
and	O
PageRank	B-Algorithm
metric	O
of	O
all	O
pages	O
that	O
link	O
to	O
it	O
(	O
"	O
incoming	O
links	O
"	O
)	O
.	O
</s>
<s>
A	O
page	O
that	O
is	O
linked	O
to	O
by	O
many	O
pages	O
with	O
high	O
PageRank	B-Algorithm
receives	O
a	O
high	O
rank	O
itself	O
.	O
</s>
<s>
Numerous	O
academic	O
papers	O
concerning	O
PageRank	B-Algorithm
have	O
been	O
published	O
since	O
Page	O
and	O
Brin	O
's	O
original	O
paper	O
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
PageRank	B-Algorithm
concept	O
may	O
be	O
vulnerable	O
to	O
manipulation	O
.	O
</s>
<s>
Research	O
has	O
been	O
conducted	O
into	O
identifying	O
falsely	O
influenced	O
PageRank	B-Algorithm
rankings	O
.	O
</s>
<s>
The	O
goal	O
is	O
to	O
find	O
an	O
effective	O
means	O
of	O
ignoring	O
links	O
from	O
documents	O
with	O
falsely	O
influenced	O
PageRank	B-Algorithm
.	O
</s>
<s>
Other	O
link-based	O
ranking	O
algorithms	O
for	O
Web	O
pages	O
include	O
the	O
HITS	B-Application
algorithm	I-Application
invented	O
by	O
Jon	O
Kleinberg	O
(	O
used	O
by	O
Teoma	B-Application
and	O
now	O
Ask.com	B-Application
)	O
,	O
the	O
IBM	O
CLEVER	B-Application
project	I-Application
,	O
the	O
TrustRank	B-Application
algorithm	O
and	O
the	O
Hummingbird	O
algorithm	O
.	O
</s>
<s>
The	O
eigenvalue	O
problem	O
behind	O
PageRank	B-Algorithm
's	O
algorithm	O
was	O
independently	O
rediscovered	O
and	O
reused	O
in	O
many	O
scoring	O
problems	O
.	O
</s>
<s>
A	O
search	B-Application
engine	I-Application
called	O
"	O
RankDex	O
"	O
from	O
IDD	O
Information	O
Services	O
,	O
designed	O
by	O
Robin	O
Li	O
in	O
1996	O
,	O
developed	O
a	O
strategy	O
for	O
site-scoring	O
and	O
page-ranking	O
.	O
</s>
<s>
RankDex	O
,	O
the	O
first	O
search	B-Application
engine	I-Application
with	O
page-ranking	O
and	O
site-scoring	O
algorithms	O
,	O
was	O
launched	O
in	O
1996	O
.	O
</s>
<s>
He	O
later	O
used	O
it	O
when	O
he	O
founded	O
Baidu	B-Application
in	O
China	O
in	O
2000	O
.	O
</s>
<s>
Google	B-Application
founder	O
Larry	O
Page	O
referenced	O
Li	O
's	O
work	O
as	O
a	O
citation	O
in	O
some	O
of	O
his	O
U.S.	O
patents	O
for	O
PageRank	B-Algorithm
.	O
</s>
<s>
Larry	O
Page	O
and	O
Sergey	O
Brin	O
developed	O
PageRank	B-Algorithm
at	O
Stanford	O
University	O
in	O
1996	O
as	O
part	O
of	O
a	O
research	O
project	O
about	O
a	O
new	O
kind	O
of	O
search	B-Application
engine	I-Application
.	O
</s>
<s>
Sergey	O
Brin	O
had	O
the	O
idea	O
that	O
information	O
on	O
the	O
web	O
could	O
be	O
ordered	O
in	O
a	O
hierarchy	O
by	O
"	O
link	O
popularity	O
"	O
:	O
a	O
page	B-Algorithm
ranks	I-Algorithm
higher	O
as	O
there	O
are	O
more	O
links	O
to	O
it	O
.	O
</s>
<s>
The	O
system	O
was	O
developed	O
with	O
the	O
help	O
of	O
Scott	O
Hassan	O
and	O
Alan	O
Steremberg	O
,	O
both	O
of	O
whom	O
were	O
cited	O
by	O
Page	O
and	O
Brin	O
as	O
being	O
critical	O
to	O
the	O
development	O
of	O
Google	B-Application
.	I-Application
</s>
<s>
Rajeev	O
Motwani	O
and	O
Terry	O
Winograd	O
co-authored	O
with	O
Page	O
and	O
Brin	O
the	O
first	O
paper	O
about	O
the	O
project	O
,	O
describing	O
PageRank	B-Algorithm
and	O
the	O
initial	O
prototype	O
of	O
the	B-Application
Google	I-Application
search	B-Application
engine	I-Application
,	O
published	O
in	O
1998	O
.	O
</s>
<s>
Shortly	O
after	O
,	O
Page	O
and	O
Brin	O
founded	O
Google	O
Inc.	O
,	O
the	O
company	O
behind	O
the	B-Application
Google	I-Application
search	B-Application
engine	I-Application
.	O
</s>
<s>
While	O
just	O
one	O
of	O
many	O
factors	O
that	O
determine	O
the	O
ranking	O
of	O
Google	B-Application
search	I-Application
results	O
,	O
PageRank	B-Algorithm
continues	O
to	O
provide	O
the	O
basis	O
for	O
all	O
of	O
Google	B-Application
's	I-Application
web-search	O
tools	O
.	O
</s>
<s>
The	O
name	O
"	O
PageRank	B-Algorithm
"	O
plays	O
on	O
the	O
name	O
of	O
developer	O
Larry	O
Page	O
,	O
as	O
well	O
as	O
of	O
the	O
concept	O
of	O
a	O
web	O
page	O
.	O
</s>
<s>
The	O
word	O
is	O
a	O
trademark	O
of	O
Google	B-Application
,	O
and	O
the	O
PageRank	B-Algorithm
process	O
has	O
been	O
patented	O
(	O
)	O
.	O
</s>
<s>
However	O
,	O
the	O
patent	O
is	O
assigned	O
to	O
Stanford	O
University	O
and	O
not	O
to	O
Google	B-Application
.	I-Application
</s>
<s>
Google	B-Application
has	O
exclusive	O
license	O
rights	O
on	O
the	O
patent	O
from	O
Stanford	O
University	O
.	O
</s>
<s>
The	O
university	O
received	O
1.8	O
million	O
shares	O
of	O
Google	B-Application
in	O
exchange	O
for	O
use	O
of	O
the	O
patent	O
;	O
it	O
sold	O
the	O
shares	O
in	O
2005	O
for	O
US$336	O
million	O
.	O
</s>
<s>
PageRank	B-Algorithm
was	O
influenced	O
by	O
citation	O
analysis	O
,	O
early	O
developed	O
by	O
Eugene	O
Garfield	O
in	O
the	O
1950s	O
at	O
the	O
University	O
of	O
Pennsylvania	O
,	O
and	O
by	O
Hyper	O
Search	O
,	O
developed	O
by	O
Massimo	O
Marchiori	O
at	O
the	O
University	O
of	O
Padua	O
.	O
</s>
<s>
In	O
the	O
same	O
year	O
PageRank	B-Algorithm
was	O
introduced	O
(	O
1998	O
)	O
,	O
Jon	O
Kleinberg	O
published	O
his	O
work	O
on	O
HITS	B-Application
.	O
</s>
<s>
Google	B-Application
's	I-Application
founders	O
cite	O
Garfield	O
,	O
Marchiori	O
,	O
and	O
Kleinberg	O
in	O
their	O
original	O
papers	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
algorithm	I-Algorithm
outputs	O
a	O
probability	O
distribution	O
used	O
to	O
represent	O
the	O
likelihood	O
that	O
a	O
person	O
randomly	O
clicking	O
on	O
links	O
will	O
arrive	O
at	O
any	O
particular	O
page	O
.	O
</s>
<s>
PageRank	B-Algorithm
can	O
be	O
calculated	O
for	O
collections	O
of	O
documents	O
of	O
any	O
size	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
computations	O
require	O
several	O
passes	O
,	O
called	O
"	O
iterations	O
"	O
,	O
through	O
the	O
collection	O
to	O
adjust	O
approximate	O
PageRank	B-Algorithm
values	O
to	O
more	O
closely	O
reflect	O
the	O
theoretical	O
true	O
value	O
.	O
</s>
<s>
Hence	O
,	O
a	O
document	O
with	O
a	O
PageRank	B-Algorithm
of	O
0.5	O
means	O
there	O
is	O
a	O
50%	O
chance	O
that	O
a	O
person	O
clicking	O
on	O
a	O
random	O
link	O
will	O
be	O
directed	O
to	O
said	O
document	O
.	O
</s>
<s>
PageRank	B-Algorithm
is	O
initialized	O
to	O
the	O
same	O
value	O
for	O
all	O
pages	O
.	O
</s>
<s>
In	O
the	O
original	O
form	O
of	O
PageRank	B-Algorithm
,	O
the	O
sum	O
of	O
PageRank	B-Algorithm
over	O
all	O
pages	O
was	O
the	O
total	O
number	O
of	O
pages	O
on	O
the	O
web	O
at	O
that	O
time	O
,	O
so	O
each	O
page	O
in	O
this	O
example	O
would	O
have	O
an	O
initial	O
value	O
of	O
1	O
.	O
</s>
<s>
However	O
,	O
later	O
versions	O
of	O
PageRank	B-Algorithm
,	O
and	O
the	O
remainder	O
of	O
this	O
section	O
,	O
assume	O
a	O
probability	O
distribution	O
between	O
0	O
and	O
1	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
transferred	O
from	O
a	O
given	O
page	O
to	O
the	O
targets	O
of	O
its	O
outbound	O
links	O
upon	O
the	O
next	O
iteration	O
is	O
divided	O
equally	O
among	O
all	O
outbound	O
links	O
.	O
</s>
<s>
If	O
the	O
only	O
links	O
in	O
the	O
system	O
were	O
from	O
pages	O
B	O
,	O
C	O
,	O
and	O
D	O
to	O
A	O
,	O
each	O
link	O
would	O
transfer	O
0.25	O
PageRank	B-Algorithm
to	O
A	O
upon	O
the	O
next	O
iteration	O
,	O
for	O
a	O
total	O
of	O
0.75	O
.	O
</s>
<s>
At	O
the	O
completion	O
of	O
this	O
iteration	O
,	O
page	O
A	O
will	O
have	O
a	O
PageRank	B-Algorithm
of	O
approximately	O
0.458	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
the	O
PageRank	B-Algorithm
conferred	O
by	O
an	O
outbound	O
link	O
is	O
equal	O
to	O
the	O
document	O
's	O
own	O
PageRank	B-Algorithm
score	O
divided	O
by	O
the	O
number	O
of	O
outbound	O
links	O
L( )	O
.	O
</s>
<s>
In	O
the	O
general	O
case	O
,	O
the	O
PageRank	B-Algorithm
value	O
for	O
any	O
page	O
u	O
can	O
be	O
expressed	O
as	O
:	O
</s>
<s>
the	O
PageRank	B-Algorithm
value	O
for	O
a	O
page	O
u	O
is	O
dependent	O
on	O
the	O
PageRank	B-Algorithm
values	O
for	O
each	O
page	O
v	O
contained	O
in	O
the	O
set	O
Bu	O
(	O
the	O
set	O
containing	O
all	O
pages	O
linking	O
to	O
page	O
u	O
)	O
,	O
divided	O
by	O
the	O
number	O
L(v )	O
of	O
links	O
from	O
page	O
v	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
theory	O
holds	O
that	O
an	O
imaginary	O
surfer	O
who	O
is	O
randomly	O
clicking	O
on	O
links	O
will	O
eventually	O
stop	O
clicking	O
.	O
</s>
<s>
The	O
damping	O
factor	O
is	O
subtracted	O
from	O
1	O
(	O
and	O
in	O
some	O
variations	O
of	O
the	O
algorithm	O
,	O
the	O
result	O
is	O
divided	O
by	O
the	O
number	O
of	O
documents	O
(	O
N	O
)	O
in	O
the	O
collection	O
)	O
and	O
this	O
term	O
is	O
then	O
added	O
to	O
the	O
product	O
of	O
the	O
damping	O
factor	O
and	O
the	O
sum	O
of	O
the	O
incoming	O
PageRank	B-Algorithm
scores	O
.	O
</s>
<s>
So	O
any	O
page	O
's	O
PageRank	B-Algorithm
is	O
derived	O
in	O
large	O
part	O
from	O
the	O
PageRanks	B-Algorithm
of	O
other	O
pages	O
.	O
</s>
<s>
The	O
difference	O
between	O
them	O
is	O
that	O
the	O
PageRank	B-Algorithm
values	O
in	O
the	O
first	O
formula	O
sum	O
to	O
one	O
,	O
while	O
in	O
the	O
second	O
formula	O
each	O
PageRank	B-Algorithm
is	O
multiplied	O
by	O
N	O
and	O
the	O
sum	O
becomes	O
N	O
.	O
A	O
statement	O
in	O
Page	O
and	O
Brin	O
's	O
paper	O
that	O
"	O
the	O
sum	O
of	O
all	O
PageRanks	B-Algorithm
is	O
one	O
"	O
and	O
claims	O
by	O
other	O
Google	B-Application
employees	O
support	O
the	O
first	O
variant	O
of	O
the	O
formula	O
above	O
.	O
</s>
<s>
Page	O
and	O
Brin	O
confused	O
the	O
two	O
formulas	O
in	O
their	O
most	O
popular	O
paper	O
"	O
The	O
Anatomy	O
of	O
a	O
Large-Scale	O
Hypertextual	O
Web	B-Application
Search	I-Application
Engine	I-Application
"	O
,	O
where	O
they	O
mistakenly	O
claimed	O
that	O
the	O
latter	O
formula	O
formed	O
a	O
probability	O
distribution	O
over	O
web	O
pages	O
.	O
</s>
<s>
Google	B-Application
recalculates	O
PageRank	B-Algorithm
scores	O
each	O
time	O
it	O
crawls	O
the	O
Web	O
and	O
rebuilds	O
its	O
index	O
.	O
</s>
<s>
As	O
Google	B-Application
increases	O
the	O
number	O
of	O
documents	O
in	O
its	O
collection	O
,	O
the	O
initial	O
approximation	O
of	O
PageRank	B-Algorithm
decreases	O
for	O
all	O
documents	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
value	O
of	O
a	O
page	O
reflects	O
the	O
chance	O
that	O
the	O
random	O
surfer	O
will	O
land	O
on	O
that	O
page	O
by	O
clicking	O
on	O
a	O
link	O
.	O
</s>
<s>
When	O
calculating	O
PageRank	B-Algorithm
,	O
pages	O
with	O
no	O
outbound	O
links	O
are	O
assumed	O
to	O
link	O
out	O
to	O
all	O
other	O
pages	O
in	O
the	O
collection	O
.	O
</s>
<s>
Their	O
PageRank	B-Algorithm
scores	O
are	O
therefore	O
divided	O
evenly	O
among	O
all	O
other	O
pages	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
values	O
are	O
the	O
entries	O
of	O
the	O
dominant	O
right	O
eigenvector	O
of	O
the	O
modified	B-Algorithm
adjacency	I-Algorithm
matrix	I-Algorithm
rescaled	O
so	O
that	O
each	O
column	O
adds	O
up	O
to	O
one	O
.	O
</s>
<s>
the	O
elements	O
of	O
each	O
column	O
sum	O
up	O
to	O
1	O
,	O
so	O
the	O
matrix	O
is	O
a	O
stochastic	B-Algorithm
matrix	I-Algorithm
(	O
for	O
more	O
details	O
see	O
the	O
computation	O
section	O
below	O
)	O
.	O
</s>
<s>
Because	O
of	O
the	O
large	O
eigengap	O
of	O
the	O
modified	B-Algorithm
adjacency	I-Algorithm
matrix	I-Algorithm
above	O
,	O
the	O
values	O
of	O
the	O
PageRank	B-Algorithm
eigenvector	O
can	O
be	O
approximated	O
to	O
within	O
a	O
high	O
degree	O
of	O
accuracy	O
within	O
only	O
a	O
few	O
iterations	O
.	O
</s>
<s>
Google	B-Application
's	I-Application
founders	O
,	O
in	O
their	O
original	O
paper	O
,	O
reported	O
that	O
the	O
PageRank	B-Algorithm
algorithm	I-Algorithm
for	O
a	O
network	O
consisting	O
of	O
322	O
million	O
links	O
(	O
in-edges	O
and	O
out-edges	O
)	O
converges	O
to	O
within	O
a	O
tolerable	O
limit	O
in	O
52	O
iterations	O
.	O
</s>
<s>
As	O
a	O
result	O
of	O
Markov	O
theory	O
,	O
it	O
can	O
be	O
shown	O
that	O
the	O
PageRank	B-Algorithm
of	O
a	O
page	O
is	O
the	O
probability	O
of	O
arriving	O
at	O
that	O
page	O
after	O
a	O
large	O
number	O
of	O
clicks	O
.	O
</s>
<s>
One	O
main	O
disadvantage	O
of	O
PageRank	B-Algorithm
is	O
that	O
it	O
favors	O
older	O
pages	O
.	O
</s>
<s>
Several	O
strategies	O
have	O
been	O
proposed	O
to	O
accelerate	O
the	O
computation	O
of	O
PageRank	B-Algorithm
.	O
</s>
<s>
Various	O
strategies	O
to	O
manipulate	O
PageRank	B-Algorithm
have	O
been	O
employed	O
in	O
concerted	O
efforts	O
to	O
improve	O
search	B-Application
results	I-Application
rankings	O
and	O
monetize	O
advertising	O
links	O
.	O
</s>
<s>
These	O
strategies	O
have	O
severely	O
impacted	O
the	O
reliability	O
of	O
the	O
PageRank	B-Algorithm
concept	O
,	O
which	O
purports	O
to	O
determine	O
which	O
documents	O
are	O
actually	O
highly	O
valued	O
by	O
the	O
Web	O
community	O
.	O
</s>
<s>
Since	O
December	O
2007	O
,	O
when	O
it	O
started	O
actively	O
penalizing	O
sites	O
selling	O
paid	O
text	O
links	O
,	O
Google	B-Application
has	O
combatted	O
link	O
farms	O
and	O
other	O
schemes	O
designed	O
to	O
artificially	O
inflate	O
PageRank	B-Algorithm
.	O
</s>
<s>
How	O
Google	B-Application
identifies	O
link	O
farms	O
and	O
other	O
PageRank	B-Algorithm
manipulation	O
tools	O
is	O
among	O
Google	B-Application
's	I-Application
trade	O
secrets	O
.	O
</s>
<s>
PageRank	B-Algorithm
can	O
be	O
computed	O
either	O
iteratively	O
or	O
algebraically	O
.	O
</s>
<s>
The	O
iterative	O
method	O
can	O
be	O
viewed	O
as	O
the	O
power	B-Language
iteration	I-Language
method	O
or	O
the	O
power	B-Language
method	I-Language
.	O
</s>
<s>
denotes	O
the	O
adjacency	B-Algorithm
matrix	I-Algorithm
of	O
the	O
graph	B-Application
and	O
is	O
the	O
diagonal	O
matrix	O
with	O
the	O
outdegrees	O
in	O
the	O
diagonal	O
.	O
</s>
<s>
Hence	O
PageRank	B-Algorithm
is	O
the	O
principal	O
eigenvector	O
of	O
.	O
</s>
<s>
A	O
fast	O
and	O
easy	O
way	O
to	O
compute	O
this	O
is	O
using	O
the	O
power	B-Language
method	I-Language
:	O
starting	O
with	O
an	O
arbitrary	O
vector	O
,	O
the	O
operator	O
is	O
applied	O
in	O
succession	O
,	O
i.e.	O
,	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
above	O
two	O
computations	O
using	O
only	O
give	O
the	O
same	O
PageRank	B-Algorithm
if	O
their	O
results	O
are	O
normalized	O
:	O
</s>
<s>
where	O
denotes	O
the	O
degree	O
of	O
vertex	O
,	O
and	O
is	O
the	O
edge-set	O
of	O
the	O
graph	B-Application
,	O
then	O
,	O
with	O
,	O
shows	O
that	O
:	O
</s>
<s>
that	O
is	O
,	O
the	O
PageRank	B-Algorithm
of	O
an	O
undirected	O
graph	B-Application
equals	O
to	O
the	O
degree	O
distribution	O
vector	O
if	O
and	O
only	O
if	O
the	O
graph	B-Application
is	O
regular	O
,	O
i.e.	O
,	O
every	O
vertex	O
has	O
the	O
same	O
degree	O
.	O
</s>
<s>
A	O
generalization	O
of	O
PageRank	B-Algorithm
for	O
the	O
case	O
of	O
ranking	O
two	O
interacting	O
groups	O
of	O
objects	O
was	O
described	O
by	O
Daugulis	O
.	O
</s>
<s>
describe	O
two	O
random	O
walk-based	O
distributed	B-Operating_System
algorithms	I-Operating_System
for	O
computing	O
PageRank	B-Algorithm
of	O
nodes	O
in	O
a	O
network	O
.	O
</s>
<s>
One	O
algorithm	O
takes	O
rounds	O
with	O
high	O
probability	O
on	O
any	O
graph	B-Application
(	O
directed	O
or	O
undirected	O
)	O
,	O
where	O
n	O
is	O
the	O
network	O
size	O
and	O
is	O
the	O
reset	O
probability	O
(	O
,	O
which	O
is	O
called	O
the	O
damping	O
factor	O
)	O
used	O
in	O
the	O
PageRank	B-Algorithm
computation	O
.	O
</s>
<s>
The	B-Application
Google	I-Application
Toolbar	O
long	O
had	O
a	O
PageRank	B-Algorithm
feature	O
which	O
displayed	O
a	O
visited	O
page	O
's	O
PageRank	B-Algorithm
as	O
a	O
whole	O
number	O
between	O
0	O
(	O
least	O
popular	O
)	O
and	O
10	O
(	O
most	O
popular	O
)	O
.	O
</s>
<s>
Google	B-Application
had	O
not	O
disclosed	O
the	O
specific	O
method	O
for	O
determining	O
a	O
Toolbar	O
PageRank	B-Algorithm
value	O
,	O
which	O
was	O
to	O
be	O
considered	O
only	O
a	O
rough	O
indication	O
of	O
the	O
value	O
of	O
a	O
website	O
.	O
</s>
<s>
The	O
"	O
Toolbar	O
Pagerank	B-Algorithm
"	O
was	O
available	O
for	O
verified	O
site	O
maintainers	O
through	O
the	B-Application
Google	I-Application
Webmaster	O
Tools	O
interface	O
.	O
</s>
<s>
However	O
,	O
on	O
October	O
15	O
,	O
2009	O
,	O
a	O
Google	B-Application
employee	O
confirmed	O
that	O
the	O
company	O
had	O
removed	O
PageRank	B-Algorithm
from	O
its	O
Webmaster	O
Tools	O
section	O
,	O
saying	O
that	O
"	O
We	O
've	O
been	O
telling	O
people	O
for	O
a	O
long	O
time	O
that	O
they	O
should	O
n't	O
focus	O
on	O
PageRank	B-Algorithm
so	O
much	O
.	O
</s>
<s>
The	O
"	O
Toolbar	O
Pagerank	B-Algorithm
"	O
was	O
updated	O
very	O
infrequently	O
.	O
</s>
<s>
In	O
October	O
2014	O
Matt	O
Cutts	O
announced	O
that	O
another	O
visible	O
pagerank	B-Algorithm
update	O
would	O
not	O
be	O
coming	O
.	O
</s>
<s>
In	O
March	O
2016	O
Google	B-Application
announced	O
it	O
would	O
no	O
longer	O
support	O
this	O
feature	O
,	O
and	O
the	O
underlying	O
API	O
would	O
soon	O
cease	O
to	O
operate	O
.	O
</s>
<s>
On	O
April	O
15	O
,	O
2016	O
,	O
Google	B-Application
turned	O
off	O
display	O
of	O
PageRank	B-Algorithm
Data	O
in	O
Google	B-Protocol
Toolbar	I-Protocol
,	O
though	O
the	O
PageRank	B-Algorithm
continued	O
to	O
be	O
used	O
internally	O
to	O
rank	O
content	O
in	O
search	B-Application
results	I-Application
.	O
</s>
<s>
The	O
search	B-Application
engine	I-Application
results	O
page	O
(	O
SERP	O
)	O
is	O
the	O
actual	O
result	O
returned	O
by	O
a	O
search	B-Application
engine	I-Application
in	O
response	O
to	O
a	O
keyword	O
query	O
.	O
</s>
<s>
The	O
SERP	O
rank	O
of	O
a	O
web	O
page	O
is	O
a	O
function	O
not	O
only	O
of	O
its	O
PageRank	B-Algorithm
,	O
but	O
of	O
a	O
relatively	O
large	O
and	O
continuously	O
adjusted	O
set	O
of	O
factors	O
(	O
over	O
200	O
)	O
.	O
</s>
<s>
Search	B-Application
engine	I-Application
optimization	O
(	O
SEO	O
)	O
is	O
aimed	O
at	O
influencing	O
the	O
SERP	O
rank	O
for	O
a	O
website	O
or	O
a	O
set	O
of	O
web	O
pages	O
.	O
</s>
<s>
Positioning	O
of	O
a	O
webpage	O
on	O
Google	B-Application
SERPs	O
for	O
a	O
keyword	O
depends	O
on	O
relevance	O
and	O
reputation	O
,	O
also	O
known	O
as	O
authority	O
and	O
popularity	O
.	O
</s>
<s>
PageRank	B-Algorithm
is	O
Google	B-Application
's	I-Application
indication	O
of	O
its	O
assessment	O
of	O
the	O
reputation	O
of	O
a	O
webpage	O
:	O
It	O
is	O
non-keyword	O
specific	O
.	O
</s>
<s>
Google	B-Application
uses	O
a	O
combination	O
of	O
webpage	O
and	O
website	O
authority	O
to	O
determine	O
the	O
overall	O
authority	O
of	O
a	O
webpage	O
competing	O
for	O
a	O
keyword	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
of	O
the	O
HomePage	O
of	O
a	O
website	O
is	O
the	O
best	O
indication	O
Google	B-Application
offers	O
for	O
website	O
authority	O
.	O
</s>
<s>
After	O
the	O
introduction	O
of	O
Google	B-Application
Places	I-Application
into	O
the	O
mainstream	O
organic	O
SERP	O
,	O
numerous	O
other	O
factors	O
in	O
addition	O
to	O
PageRank	B-Algorithm
affect	O
ranking	O
a	O
business	O
in	O
Local	O
Business	O
Results	O
.	O
</s>
<s>
When	O
Google	B-Application
elaborated	O
on	O
the	O
reasons	O
for	O
PageRank	B-Algorithm
deprecation	O
at	O
Q&A	O
#March	O
2016	O
,	O
they	O
announced	O
Links	O
and	O
Content	O
as	O
the	O
Top	O
Ranking	O
Factors	O
.	O
</s>
<s>
RankBrain	O
had	O
earlier	O
in	O
October	O
2015	O
been	O
announced	O
as	O
the	O
#3	O
Ranking	O
Factor	O
,	O
so	O
the	O
Top	O
3	O
Factors	O
have	O
been	O
confirmed	O
officially	O
by	O
Google	B-Application
.	I-Application
</s>
<s>
The	B-Application
Google	I-Application
Directory	O
PageRank	B-Algorithm
was	O
an	O
8-unit	O
measurement	O
.	O
</s>
<s>
Unlike	O
the	B-Application
Google	I-Application
Toolbar	O
,	O
which	O
shows	O
a	O
numeric	O
PageRank	B-Algorithm
value	O
upon	O
mouseover	O
of	O
the	O
green	O
bar	O
,	O
the	B-Application
Google	I-Application
Directory	O
only	O
displayed	O
the	O
bar	O
,	O
never	O
the	O
numeric	O
values	O
.	O
</s>
<s>
Google	B-Application
Directory	I-Application
was	O
closed	O
on	O
July	O
20	O
,	O
2011	O
.	O
</s>
<s>
It	O
was	O
known	O
that	O
the	O
PageRank	B-Algorithm
shown	O
in	O
the	O
Toolbar	O
could	O
easily	O
be	O
spoofed	O
.	O
</s>
<s>
Redirection	O
from	O
one	O
page	O
to	O
another	O
,	O
either	O
via	O
a	O
HTTP	B-Protocol
302	I-Protocol
response	O
or	O
a	O
"	O
Refresh	O
"	O
meta	O
tag	O
,	O
caused	O
the	O
source	O
page	O
to	O
acquire	O
the	O
PageRank	B-Algorithm
of	O
the	O
destination	O
page	O
.	O
</s>
<s>
Hence	O
,	O
a	O
new	O
page	O
with	O
PR	O
0	O
and	O
no	O
incoming	O
links	O
could	O
have	O
acquired	O
PR	O
10	O
by	O
redirecting	O
to	O
the	B-Application
Google	I-Application
home	O
page	O
.	O
</s>
<s>
Spoofing	O
can	O
usually	O
be	O
detected	O
by	O
performing	O
a	O
Google	B-Application
search	I-Application
for	O
a	O
source	O
URL	O
;	O
if	O
the	O
URL	O
of	O
an	O
entirely	O
different	O
site	O
is	O
displayed	O
in	O
the	O
results	O
,	O
the	O
latter	O
URL	O
may	O
represent	O
the	O
destination	O
of	O
a	O
redirection	O
.	O
</s>
<s>
For	O
search	B-Application
engine	I-Application
optimization	O
purposes	O
,	O
some	O
companies	O
offer	O
to	O
sell	O
high	O
PageRank	B-Algorithm
links	O
to	O
webmasters	O
.	O
</s>
<s>
However	O
,	O
Google	B-Application
has	O
publicly	O
warned	O
webmasters	O
that	O
if	O
they	O
are	O
or	O
were	O
discovered	O
to	O
be	O
selling	O
links	O
for	O
the	O
purpose	O
of	O
conferring	O
PageRank	B-Algorithm
and	O
reputation	O
,	O
their	O
links	O
will	O
be	O
devalued	O
(	O
ignored	O
in	O
the	O
calculation	O
of	O
other	O
pages	O
 '	O
PageRanks	B-Algorithm
)	O
.	O
</s>
<s>
Google	B-Application
advised	O
webmasters	O
to	O
use	O
the	O
nofollow	B-Application
HTML	B-General_Concept
attribute	I-General_Concept
value	O
on	O
paid	O
links	O
.	O
</s>
<s>
According	O
to	O
Matt	O
Cutts	O
,	O
Google	B-Application
is	O
concerned	O
about	O
webmasters	O
who	O
try	O
to	O
game	O
the	O
system	O
,	O
and	O
thereby	O
reduce	O
the	O
quality	O
and	O
relevance	O
of	O
Google	B-Application
search	I-Application
results	O
.	O
</s>
<s>
In	O
2019	O
,	O
Google	B-Application
offered	O
a	O
new	O
type	O
of	O
tags	O
that	O
do	O
not	O
pass	O
"	O
link	O
juice	O
"	O
and	O
thus	O
do	O
not	O
have	O
value	O
for	O
SEO	O
link	O
manipulation	O
:	O
rel	O
=	O
"	O
ugc	O
"	O
as	O
a	O
tag	O
for	O
user-generated	O
content	O
,	O
such	O
as	O
comments	O
;	O
and	O
rel	O
=	O
"	O
sponsored	O
"	O
tag	O
for	O
advertisements	O
or	O
other	O
types	O
of	O
sponsored	O
content	O
.	O
</s>
<s>
Even	O
though	O
PageRank	B-Algorithm
has	O
become	O
less	O
important	O
for	O
SEO	O
purposes	O
,	O
the	O
existence	O
of	O
back-links	O
from	O
more	O
popular	O
websites	O
continues	O
to	O
push	O
a	O
webpage	O
higher	O
up	O
in	O
search	O
rankings	O
.	O
</s>
<s>
This	O
model	O
is	O
based	O
on	O
a	O
query-dependent	O
PageRank	B-Algorithm
score	O
of	O
a	O
page	O
which	O
as	O
the	O
name	O
suggests	O
is	O
also	O
a	O
function	O
of	O
query	O
.	O
</s>
<s>
The	O
resulting	O
distribution	O
over	O
visited	O
web	O
pages	O
is	O
QD-PageRank	O
.	O
</s>
<s>
Katja	O
Mayer	O
views	O
PageRank	B-Algorithm
as	O
a	O
social	O
network	O
as	O
it	O
connects	O
differing	O
viewpoints	O
and	O
thoughts	O
in	O
a	O
single	O
place	O
.	O
</s>
<s>
People	O
go	O
to	O
PageRank	B-Algorithm
for	O
information	O
and	O
are	O
flooded	O
with	O
citations	O
of	O
other	O
authors	O
who	O
also	O
have	O
an	O
opinion	O
on	O
the	O
topic	O
.	O
</s>
<s>
There	O
is	O
a	O
social	O
relationship	O
that	O
exists	O
between	O
PageRank	B-Algorithm
and	O
the	O
people	O
who	O
use	O
it	O
as	O
it	O
is	O
constantly	O
adapting	O
and	O
changing	O
to	O
the	O
shifts	O
in	O
modern	O
society	O
.	O
</s>
<s>
Viewing	O
the	O
relationship	O
between	O
PageRank	B-Algorithm
and	O
the	O
individual	O
through	O
sociometry	O
allows	O
for	O
an	O
in-depth	O
look	O
at	O
the	O
connection	O
that	O
results	O
.	O
</s>
<s>
Matteo	O
Pasquinelli	O
reckons	O
the	O
basis	O
for	O
the	O
belief	O
that	O
PageRank	B-Algorithm
has	O
a	O
social	O
component	O
lies	O
in	O
the	O
idea	O
of	O
attention	O
economy	O
.	O
</s>
<s>
With	O
attention	O
economy	O
,	O
value	O
is	O
placed	O
on	O
products	O
that	O
receive	O
a	O
greater	O
amount	O
of	O
human	O
attention	O
and	O
the	O
results	O
at	O
the	O
top	O
of	O
the	O
PageRank	B-Algorithm
garner	O
a	O
larger	O
amount	O
of	O
focus	O
then	O
those	O
on	O
subsequent	O
pages	O
.	O
</s>
<s>
The	O
outcomes	O
with	O
the	O
higher	O
PageRank	B-Algorithm
will	O
therefore	O
enter	O
the	O
human	O
consciousness	O
to	O
a	O
larger	O
extent	O
.	O
</s>
<s>
These	O
ideas	O
can	O
influence	O
decision-making	O
and	O
the	O
actions	O
of	O
the	O
viewer	O
have	O
a	O
direct	O
relation	O
to	O
the	O
PageRank	B-Algorithm
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
of	O
these	O
sites	O
allow	O
them	O
to	O
be	O
trusted	O
and	O
they	O
are	O
able	O
to	O
parlay	O
this	O
trust	O
into	O
increased	O
business	O
.	O
</s>
<s>
The	O
mathematics	O
of	O
PageRank	B-Algorithm
are	O
entirely	O
general	O
and	O
apply	O
to	O
any	O
graph	B-Application
or	O
network	O
in	O
any	O
domain	O
.	O
</s>
<s>
Thus	O
,	O
PageRank	B-Algorithm
is	O
now	O
regularly	O
used	O
in	O
bibliometrics	O
,	O
social	O
and	O
information	O
network	O
analysis	O
,	O
and	O
for	O
link	O
prediction	O
and	O
recommendation	O
.	O
</s>
<s>
PageRank	B-Algorithm
has	O
been	O
used	O
to	O
quantify	O
the	O
scientific	O
impact	O
of	O
researchers	O
.	O
</s>
<s>
The	O
underlying	O
citation	O
and	O
collaboration	O
networks	O
are	O
used	O
in	O
conjunction	O
with	O
pagerank	B-Algorithm
algorithm	I-Algorithm
in	O
order	O
to	O
come	O
up	O
with	O
a	O
ranking	O
system	O
for	O
individual	O
publications	O
which	O
propagates	O
to	O
individual	O
authors	O
.	O
</s>
<s>
The	O
new	O
index	O
known	O
as	O
pagerank-index	O
(	O
Pi	O
)	O
is	O
demonstrated	O
to	O
be	O
fairer	O
compared	O
to	O
h-index	O
in	O
the	O
context	O
of	O
many	O
drawbacks	O
exhibited	O
by	O
h-index	O
.	O
</s>
<s>
For	O
the	O
analysis	O
of	O
protein	O
networks	O
in	O
biology	O
PageRank	B-Algorithm
is	O
also	O
a	O
useful	O
tool	O
.	O
</s>
<s>
In	O
any	O
ecosystem	O
,	O
a	O
modified	O
version	O
of	O
PageRank	B-Algorithm
may	O
be	O
used	O
to	O
determine	O
species	O
that	O
are	O
essential	O
to	O
the	O
continuing	O
health	O
of	O
the	O
environment	O
.	O
</s>
<s>
A	O
similar	O
newer	O
use	O
of	O
PageRank	B-Algorithm
is	O
to	O
rank	O
academic	O
doctoral	O
programs	O
based	O
on	O
their	O
records	O
of	O
placing	O
their	O
graduates	O
in	O
faculty	O
positions	O
.	O
</s>
<s>
In	O
PageRank	B-Algorithm
terms	O
,	O
academic	O
departments	O
link	O
to	O
each	O
other	O
by	O
hiring	O
their	O
faculty	O
from	O
each	O
other	O
(	O
and	O
from	O
themselves	O
)	O
.	O
</s>
<s>
A	O
version	O
of	O
PageRank	B-Algorithm
has	O
recently	O
been	O
proposed	O
as	O
a	O
replacement	O
for	O
the	O
traditional	O
Institute	O
for	O
Scientific	O
Information	O
(	O
ISI	O
)	O
impact	O
factor	O
,	O
and	O
implemented	O
at	O
Eigenfactor	O
as	O
well	O
as	O
at	O
SCImago	O
.	O
</s>
<s>
Instead	O
of	O
merely	O
counting	O
total	O
citations	O
to	O
a	O
journal	O
,	O
the	O
"	O
importance	O
"	O
of	O
each	O
citation	O
is	O
determined	O
in	O
a	O
PageRank	B-Algorithm
fashion	O
.	O
</s>
<s>
In	O
neuroscience	O
,	O
the	O
PageRank	B-Algorithm
of	O
a	O
neuron	O
in	O
a	O
neural	O
network	O
has	O
been	O
found	O
to	O
correlate	O
with	O
its	O
relative	O
firing	O
rate	O
.	O
</s>
<s>
Personalized	O
PageRank	B-Algorithm
is	O
used	O
by	O
Twitter	B-Application
to	O
present	O
users	O
with	O
other	O
accounts	O
they	O
may	O
wish	O
to	O
follow	O
.	O
</s>
<s>
Swiftype	B-Application
's	O
site	O
search	O
product	O
builds	O
a	O
"	O
PageRank	B-Algorithm
that	O
's	O
specific	O
to	O
individual	O
websites	O
"	O
by	O
looking	O
at	O
each	O
website	O
's	O
signals	O
of	O
importance	O
and	O
prioritizing	O
content	O
based	O
on	O
factors	O
such	O
as	O
number	O
of	O
links	O
from	O
the	O
home	O
page	O
.	O
</s>
<s>
A	O
Web	B-Application
crawler	I-Application
may	O
use	O
PageRank	B-Algorithm
as	O
one	O
of	O
a	O
number	O
of	O
importance	O
metrics	O
it	O
uses	O
to	O
determine	O
which	O
URL	O
to	O
visit	O
during	O
a	O
crawl	O
of	O
the	O
web	O
.	O
</s>
<s>
One	O
of	O
the	O
early	O
working	O
papers	O
that	O
were	O
used	O
in	O
the	O
creation	O
of	O
Google	B-Application
is	O
Efficient	O
crawling	O
through	O
URL	O
ordering	O
,	O
which	O
discusses	O
the	O
use	O
of	O
a	O
number	O
of	O
different	O
importance	O
metrics	O
to	O
determine	O
how	O
deeply	O
,	O
and	O
how	O
much	O
of	O
a	O
site	O
Google	B-Application
will	O
crawl	O
.	O
</s>
<s>
PageRank	B-Algorithm
is	O
presented	O
as	O
one	O
of	O
a	O
number	O
of	O
these	O
importance	O
metrics	O
,	O
though	O
there	O
are	O
others	O
listed	O
such	O
as	O
the	O
number	O
of	O
inbound	O
and	O
outbound	O
links	O
for	O
a	O
URL	O
,	O
and	O
the	O
distance	O
from	O
the	O
root	O
directory	O
on	O
a	O
site	O
to	O
the	O
URL	O
.	O
</s>
<s>
The	O
PageRank	B-Algorithm
may	O
also	O
be	O
used	O
as	O
a	O
methodology	O
to	O
measure	O
the	O
apparent	O
impact	O
of	O
a	O
community	O
like	O
the	O
Blogosphere	O
on	O
the	O
overall	O
Web	O
itself	O
.	O
</s>
<s>
This	O
approach	O
uses	O
therefore	O
the	O
PageRank	B-Algorithm
to	O
measure	O
the	O
distribution	O
of	O
attention	O
in	O
reflection	O
of	O
the	O
Scale-free	O
network	O
paradigm	O
.	O
</s>
<s>
SD2	O
uses	O
PageRank	B-Algorithm
for	O
the	O
processing	O
of	O
the	O
transitive	O
proxy	O
votes	O
,	O
with	O
the	O
additional	O
constraints	O
of	O
mandating	O
at	O
least	O
two	O
initial	O
proxies	O
per	O
voter	O
,	O
and	O
all	O
voters	O
are	O
proxy	O
candidates	O
.	O
</s>
<s>
In	O
sport	O
the	O
PageRank	B-Algorithm
algorithm	I-Algorithm
has	O
been	O
used	O
to	O
rank	O
the	O
performance	O
of	O
:	O
teams	O
in	O
the	O
National	O
Football	O
League	O
(	O
NFL	O
)	O
in	O
the	O
USA	O
;	O
individual	O
soccer	O
players	O
;	O
and	O
athletes	O
in	O
the	O
Diamond	O
League	O
.	O
</s>
<s>
PageRank	B-Algorithm
has	O
been	O
used	O
to	O
rank	O
spaces	O
or	O
streets	O
to	O
predict	O
how	O
many	O
people	O
(	O
pedestrians	O
or	O
vehicles	O
)	O
come	O
to	O
the	O
individual	O
spaces	O
or	O
streets	O
.	O
</s>
<s>
In	O
lexical	O
semantics	O
it	O
has	O
been	O
used	O
to	O
perform	O
Word	B-General_Concept
Sense	I-General_Concept
Disambiguation	I-General_Concept
,	O
Semantic	O
similarity	O
,	O
and	O
also	O
to	O
automatically	O
rank	O
WordNet	B-General_Concept
synsets	B-General_Concept
according	O
to	O
how	O
strongly	O
they	O
possess	O
a	O
given	O
semantic	O
property	O
,	O
such	O
as	O
positivity	O
or	O
negativity	O
.	O
</s>
<s>
In	O
early	O
2005	O
,	O
Google	B-Application
implemented	O
a	O
new	O
value	O
,	O
"	O
nofollow	B-Application
"	O
,	O
for	O
the	O
rel	O
attribute	O
of	O
HTML	O
link	O
and	O
anchor	O
elements	O
,	O
so	O
that	O
website	O
developers	O
and	O
bloggers	O
can	O
make	O
links	O
that	O
Google	B-Application
will	O
not	O
consider	O
for	O
the	O
purposes	O
of	O
PageRank	B-Algorithm
—	O
they	O
are	O
links	O
that	O
no	O
longer	O
constitute	O
a	O
"	O
vote	O
"	O
in	O
the	O
PageRank	B-Algorithm
system	O
.	O
</s>
<s>
The	O
nofollow	B-Application
relationship	O
was	O
added	O
in	O
an	O
attempt	O
to	O
help	O
combat	O
spamdexing	O
.	O
</s>
<s>
As	O
an	O
example	O
,	O
people	O
could	O
previously	O
create	O
many	O
message-board	O
posts	O
with	O
links	O
to	O
their	O
website	O
to	O
artificially	O
inflate	O
their	O
PageRank	B-Algorithm
.	O
</s>
<s>
With	O
the	O
nofollow	B-Application
value	O
,	O
message-board	O
administrators	O
can	O
modify	O
their	O
code	O
to	O
automatically	O
insert	O
"	O
rel='nofollow'	O
"	O
to	O
all	O
hyperlinks	O
in	O
posts	O
,	O
thus	O
preventing	O
PageRank	B-Algorithm
from	O
being	O
affected	O
by	O
those	O
particular	O
posts	O
.	O
</s>
<s>
In	O
an	O
effort	O
to	O
manually	O
control	O
the	O
flow	O
of	O
PageRank	B-Algorithm
among	O
pages	O
within	O
a	O
website	O
,	O
many	O
webmasters	O
practice	O
what	O
is	O
known	O
as	O
PageRank	B-Algorithm
Sculpting	O
—	O
which	O
is	O
the	O
act	O
of	O
strategically	O
placing	O
the	O
nofollow	B-Application
attribute	O
on	O
certain	O
internal	O
links	O
of	O
a	O
website	O
in	O
order	O
to	O
funnel	O
PageRank	B-Algorithm
towards	O
those	O
pages	O
the	O
webmaster	O
deemed	O
most	O
important	O
.	O
</s>
<s>
This	O
tactic	O
had	O
been	O
used	O
since	O
the	O
inception	O
of	O
the	O
nofollow	B-Application
attribute	O
,	O
but	O
may	O
no	O
longer	O
be	O
effective	O
since	O
Google	B-Application
announced	O
that	O
blocking	O
PageRank	B-Algorithm
transfer	O
with	O
nofollow	B-Application
does	O
not	O
redirect	O
that	O
PageRank	B-Algorithm
to	O
other	O
links	O
.	O
</s>
