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Re: [igraph] Scale free graphs -best option?

From: Szabolcs Horvát
Subject: Re: [igraph] Scale free graphs -best option?
Date: Mon, 7 Oct 2019 12:56:09 +0200

On Mon, 7 Oct 2019 at 12:05, Frederico Mestre <address@hidden> wrote:
Hello everybody,

I'm using  igraph to generate scale free graphs (I need to generate scale free graphs with a given number of nodes and links),

A "scale-free network" is one that has a power-law degree distribution.
but I have one question:

Which is the difference between these two functions?


Which would be best for this purpose?

Most of the models you find, such as preferential attachment, are based on a *process* that creates the network, and not on the *kind of network* (i.e. scale-free) that we want to create. Any given process might create networks which are scale-free, but it may not be able to create *all* scale-free networks with a given exponent, or it might create some of them with much lower probability than others.  For example, the preferential attachment model will only create connected networks.  Most networks with the same degrees will not be connected.

Thus you need to think about what you really need.

If you take one such process, and obtain some results networks created by it, you cannot claim that result for *all* scale-free networks.

To try to cover all such networks, you can try one of two things:

 - Generate one network and rewire it while keeping its degree sequence. This will sample *approximately uniformly* from the set of graphs with the same degrees.
 - Use static.power.law.game, which creates graphs where the *expected* degrees have a power-law distribution (the individual graphs may not).

To sum up, you need to think carefully why you want to do this. As Tamás said, the specific application will decide what the most reasonable approach is.

Frederico Mestre
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