Re: [igraph] problems in generating scale-free networks

[Gábor Csárdi]

Mario, try to generate denser graphs, this can be done independently
of the exponent of the power-law degree distribution.
E.g. simply

degs <- degs * 2

might be enough if you don't care about not having vertices with degree 1.

G.

On Tue, Oct 21, 2008 at 12:39 PM, Mario Lavezzi <address@hidden> wrote:
> Hi
>
> I need to generate scale-free networks with different exponents.
>
> Following previous suggestions by Gabor, I am using these commands
>
> degs <- sample(1:n, n, replace=TRUE, prob=(1:n)^(-scale))
>   if (sum(degs) %% 2 != 0) { degs[1] <- degs[1] + 1 }
>   g5 <- degree.sequence.game(degs, method="vl")
>   all(degree(g5) == degs)
>
> where "scale" is my exponent (set by me, along with other parameters).--
>
> So far, I have simulated networks with 2000 agents and, with parameters
> between 2 and 2.5 I did not find particular problems in obtaining a network
> structure.
>
> However, I noticed that, moving from 2.5 to higher values, the algorithm
> finds more and more difficult to generate a network structure, and I get the
> message:
>
> graph::make_connected() failed : #edges < #vertices-1
> Errore in degree.sequence.game(degs, method = "vl") :
>  At gengraph_mr-connected.cpp:141 : Cannot make a connected graph from the
> given degree sequence, Invalid value
>
> So far, I have tried to circumvent this by changing the seed of the random
> generator with the instruction:
>
> mySeed=33
> set.seed(mySeed, kind = NULL)
>
> I change the "mySeed" parameter and restart the program, until the algorithm
> works and a network is generated.
>
> However, with exponents >= 2.5 it takes a very high number of attempts to
> get it to work.
>
> I tried with higher (or much higher) numbers of agents, but it seems that
> little changes.
>
> I would like to reach an exponent of about 3, 3.2.
>
> Any suggestion?
>
> Thanks to all
> 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
>
>
>
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-- 
Gabor Csardi <address@hidden>     UNIL DGM