<s>
The	O
initial	B-Algorithm
attractiveness	I-Algorithm
is	O
a	O
possible	O
extension	O
of	O
the	O
Barabási	O
–	O
Albert	O
model	O
(	O
preferential	O
attachment	O
model	O
)	O
.	O
</s>
<s>
The	O
inclusion	O
of	O
initial	B-Algorithm
attractiveness	I-Algorithm
in	O
the	O
Barabási	O
–	O
Albert	O
model	O
addresses	O
the	O
low-degree	O
cut-off	O
phenomenon	O
.	O
</s>
<s>
The	O
constant	O
denotes	O
the	O
initial	B-Algorithm
attractiveness	I-Algorithm
of	O
the	O
node	O
.	O
</s>
<s>
From	O
this	O
the	O
preferential	O
attachment	O
rule	O
with	O
initial	B-Algorithm
attractiveness	I-Algorithm
comes	O
as	O
:	O
</s>
<s>
The	O
presence	O
of	O
initial	B-Algorithm
attractiveness	I-Algorithm
results	O
in	O
two	O
important	O
consequences	O
one	O
is	O
the	O
small	O
degree	O
cut-off	O
(	O
or	O
small	O
degree	O
saturation	O
)	O
.	O
</s>
<s>
The	O
reason	O
why	O
this	O
appears	O
is	O
the	O
following	O
:	O
initial	B-Algorithm
attractiveness	I-Algorithm
increases	O
the	O
probability	O
that	O
the	O
node	O
obtains	O
connection	O
with	O
an	O
arriving	O
node	O
.	O
</s>
<s>
The	O
degree	O
distribution	O
of	O
a	O
model	O
with	O
initial	B-Algorithm
attractiveness	I-Algorithm
can	O
be	O
described	O
by	O
the	O
following	O
:	O
.	O
</s>
<s>
In	O
case	O
of	O
the	O
Barabási	O
–	O
Albert	O
model	O
with	O
initial	B-Algorithm
attractiveness	I-Algorithm
the	O
degree	O
exponent	O
is	O
simply	O
.	O
</s>
<s>
The	O
same	O
holds	O
for	O
the	O
value	O
of	O
the	O
initial	B-Algorithm
attractiveness	I-Algorithm
as	O
is	O
higher	O
the	O
more	O
the	O
network	O
is	O
into	O
the	O
random	O
network	O
regime	O
.	O
</s>
