[igraph] problems in generating scale-free networks

[Mario Lavezzi]

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