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

[Mario Lavezzi]

Hello Gabor
thank you so much.

I think I got confused by the different notation used in the papers I am 
considering at the moment.
> It is still not the formula in the Dorogovtsev paper, though. I don't 
> know why, maybe they don't consider multiple edges, or the results are 
> only valid in some limit.
>   
I think that things are a little different because, they actually allow 
multiple (directed) links, consider a parameter of "attractiveness" of a 
node which is only initial (and so it is not used at each time step as 
the "zero.appeal" value, as I understand).

One last question: can you suggest a quick way of generating degree 
sequences with a given power-law exponent to  be used  in  the  
"degree.sequence.game"?
> If you just want to have graphs with various power law degree distributions,
> you might consider using 'degree.sequence.game', with method="vl", here
> you can prescribe the exact degree distribution. It always generated 
> connected graphs, but probably this is not a problem.
>
>   
Thanks a lot!
best,
Mario

> Best,
> Gabor
>
> On Mon, Sep 08, 2008 at 05:05:35PM +0200, Mario Lavezzi wrote:
>   
> > 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
> >
> >
> >
> > _______________________________________________
> > igraph-help mailing list
> > address@hidden
> > http://lists.nongnu.org/mailman/listinfo/igraph-help
> >     
>
>   

--
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