<s>
Hierarchical	B-Algorithm
clustering	I-Algorithm
is	O
one	O
method	O
for	O
finding	O
community	O
structures	O
in	O
a	O
network	O
.	O
</s>
<s>
The	O
technique	O
arranges	O
the	O
network	O
into	O
a	O
hierarchy	O
of	O
groups	O
according	O
to	O
a	O
specified	O
weight	B-General_Concept
function	O
.	O
</s>
<s>
The	O
data	O
can	O
then	O
be	O
represented	O
in	O
a	O
tree	B-Data_Structure
structure	I-Data_Structure
known	O
as	O
a	O
dendrogram	B-Application
.	O
</s>
<s>
Hierarchical	B-Algorithm
clustering	I-Algorithm
can	O
either	O
be	O
agglomerative	B-Algorithm
or	O
divisive	O
depending	O
on	O
whether	O
one	O
proceeds	O
through	O
the	O
algorithm	O
by	O
adding	O
links	O
to	O
or	O
removing	O
links	O
from	O
the	O
network	O
,	O
respectively	O
.	O
</s>
<s>
In	O
the	O
hierarchical	B-Algorithm
clustering	I-Algorithm
algorithm	O
,	O
a	O
weight	B-General_Concept
is	O
first	O
assigned	O
to	O
each	O
pair	O
of	O
vertices	O
in	O
the	O
network	O
.	O
</s>
<s>
The	O
weight	B-General_Concept
,	O
which	O
can	O
vary	O
depending	O
on	O
implementation	O
(	O
see	O
section	O
below	O
)	O
,	O
is	O
intended	O
to	O
indicate	O
how	O
closely	O
related	O
the	O
vertices	O
are	O
.	O
</s>
<s>
Then	O
,	O
starting	O
with	O
all	O
the	O
nodes	O
in	O
the	O
network	O
disconnected	O
,	O
begin	O
pairing	O
nodes	O
in	O
order	O
of	O
decreasing	O
weight	B-General_Concept
between	O
the	O
pairs	O
(	O
in	O
the	O
divisive	O
case	O
,	O
start	O
from	O
the	O
original	O
network	O
and	O
remove	O
links	O
in	O
order	O
of	O
decreasing	O
weight	B-General_Concept
)	O
.	O
</s>
<s>
Hence	O
,	O
the	O
subsets	O
can	O
be	O
represented	O
using	O
a	O
tree	O
diagram	O
,	O
or	O
dendrogram	B-Application
.	O
</s>
<s>
Horizontal	O
slices	O
of	O
the	O
tree	O
at	O
a	O
given	O
level	O
indicate	O
the	O
communities	O
that	O
exist	O
above	O
and	O
below	O
a	O
value	O
of	O
the	O
weight	B-General_Concept
.	O
</s>
<s>
There	O
are	O
many	O
possible	O
weights	O
for	O
use	O
in	O
hierarchical	B-Algorithm
clustering	I-Algorithm
algorithms	O
.	O
</s>
<s>
The	O
specific	O
weight	B-General_Concept
used	O
is	O
dictated	O
by	O
the	O
data	O
as	O
well	O
as	O
considerations	O
for	O
computational	O
speed	O
.	O
</s>
<s>
Additionally	O
,	O
the	O
communities	O
found	O
in	O
the	O
network	O
are	O
highly	O
dependent	O
on	O
the	O
choice	O
of	O
weighting	B-General_Concept
function	O
.	O
</s>
<s>
Hence	O
,	O
when	O
compared	O
to	O
real-world	O
data	O
with	O
a	O
known	O
community	O
structure	O
,	O
the	O
various	O
weighting	B-General_Concept
techniques	O
have	O
been	O
met	O
with	O
varying	O
degrees	O
of	O
success	O
.	O
</s>
<s>
One	O
disadvantage	O
of	O
these	O
weights	O
,	O
however	O
,	O
is	O
that	O
both	O
weighting	B-General_Concept
schemes	O
tend	O
to	O
separate	O
single	O
peripheral	O
vertices	O
from	O
their	O
rightful	O
communities	O
because	O
of	O
the	O
small	O
number	O
of	O
paths	O
going	O
to	O
these	O
vertices	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
their	O
use	O
in	O
hierarchical	B-Algorithm
clustering	I-Algorithm
techniques	O
is	O
far	O
from	O
optimal	O
.	O
</s>
<s>
Edge	O
betweenness	O
centrality	O
has	O
been	O
used	O
successfully	O
as	O
a	O
weight	B-General_Concept
in	O
the	O
Girvan	O
–	O
Newman	O
algorithm	O
.	O
</s>
<s>
This	O
technique	O
is	O
similar	O
to	O
a	O
divisive	O
hierarchical	B-Algorithm
clustering	I-Algorithm
algorithm	O
,	O
except	O
the	O
weights	O
are	O
recalculated	O
with	O
each	O
step	O
.	O
</s>
<s>
The	O
change	O
in	O
modularity	O
of	O
the	O
network	O
with	O
the	O
addition	O
of	O
a	O
node	O
has	O
also	O
been	O
used	O
successfully	O
as	O
a	O
weight	B-General_Concept
.	O
</s>
