# Re: [R] Watts Strogatz game

From: Gábor Csárdi <csardi_at_rmki.kfki.hu>
Date: Wed, 04 May 2011 10:25:47 -0400

On Wed, May 4, 2011 at 9:28 AM, Robert Baer <rbaer_at_atsu.edu> wrote:
>>> I have a erdos-renyi game with 6000 nodes and probability 0.003.
>>>
>>> g1 = erdos.renyi.game(6000, 0.003)
>>>
>>> How to create a Watts Strogatz game with the same probability.
>>>
>>> g1 = watts.strogatz.game(1, 6000, ?, ?)
>>> What should be the third and fourth parameter to this argument.

You can work out the number of edges in a Watts-Strogatz game easily, by calculating the degree of the nodes in the non-randomized network. This will be different for different dimensions, of course. Randomization does not change the average degree.

Obviously, you cannot exactly match all Erdos-Renyi graphs, because the W-S density cannot change continuously.

Gabor

> According to ?watts.strogatz.game help file (in the igraph package?), the
> four arguments to this function are:
> dim     Integer constant, the dimension of the starting lattice.
> size     Integer constant, the size of the lattice along each dimension.
> nei     Integer constant, the neighborhood within which the vertices of the
> lattice will be connected.
> p         Real constant between zero and one, the rewiring probability.
>
> So it looks like the last two should be neighborhood and rewiring
> probability respectively.
>
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> and provide commented, minimal, self-contained, reproducible code.
>

```--
Gabor Csardi <csardi_at_rmki.kfki.hu>     MTA KFKI RMKI

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