[igraph] problems with parameters in barabasi.game()

[Mario Lavezzi]

Hello

I am trying to generate Scale-free graphs with barabasi.game()

What I want is an undirected graph for n agents, with neither loops, nor 
multiple edges.

I would like to generate different power-law distributions with 
different exponents (ALPHA) by manipulating the "a" coefficient in the 
formula (taken from the igraph documentation, page 18):

P[i] ~ k(i)^alpha + a

Since an exponent alpha different from 1 does not generate power laws, I 
keep it fixed at 1, so I work with:

P[i] ~ k(i) + a

_Example
_
What I write:
>networkScFr = 
barabasi.game(100000,directed=FALSE,out.pref=TRUE,power=1,zero.appeal=1,m=4)
>networkScFrS = simplify(networkScFr, remove.multiple = TRUE, 
remove.loops = TRUE)
>power.law.fit(degScFr,xmin=10)
  
_What I get:_
power.law.fit(degScFr,xmin=10)

Call:
mle(minuslogl = mlogl, start = list(alpha = start))

Coefficients:
  alpha
2.970474


*_Question 1:
_*With zero.appeal = 1, I am considering

P[i] ~ k(i) + 1

which is not exactly the original BA model, which studied P[i] ~ k(i).
This is the extension proposed in http://arxiv.org/abs/cond-mat/0009090.
According to Dorogovstev et al, the power-law exponent should equal 2 + 
a/m, where m is the number of links added at each time step.
So, I should get ALPHA approx equal to 2.2, while I get ALPHA=2.97.
Am I correct? If not, where I am wrong?

*_Question 2:
_*I want to try with:

P[i] ~ k_i + 2

_What I write:_
> networkScFr = 
barabasi.game(n,directed=FALSE,out.pref=TRUE,power=1,zero.appeal=2,m=4)

_What I get:_

Warning message:
In barabasi.game(n, directed = FALSE, out.pref = TRUE, power = 1,  :
 `zero.appeal' is set to 1 for traditional BA game

Does this mean that the zero.appeal value is fixed at 1? How can I 
change it?

If I try to compute the exponent, I get:

>power.law.fit(degScFr,xmin=10)

Call:
mle(minuslogl = mlogl, start = list(alpha = start))

Coefficients:
  alpha
3.042824

That is, I obtain ALPHA=3.04, while I expected ALPHA= 2+2/4 = 2.5.

Can anyone help?

Thanks!
Mario

--
Andrea Mario Lavezzi
Dipartimento di Studi su Politica, Diritto e Società
Università di Palermo
Piazza Bologni 8
90134 Palermo, Italy
tel. ++39 091 6625600
fax ++39 091 6112023
skype: lavezzimario
email: lavezzi (at) unipa.it
web: http://www.unipa.it/~lavezzi