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## Re: [igraph] Watts-Strogaz not converging

**From**: |
Tamás Nepusz |

**Subject**: |
Re: [igraph] Watts-Strogaz not converging |

**Date**: |
Tue, 28 Jan 2014 11:10:31 +0100 |

>* I am simulating a network using Watts-Strogaz as follows:*
>* *
>* modelGraph = igraph.Graph.Watts_Strogatz(1, g.vcount(), x, prob)*
>* *
>* I need a node a vertex eccentricity value <=6*
Okay, let me know if I understand this correctly. Do you want to generate a
graph with the Watts-Strogatz model and ensure that at least one vertex has an
eccentricity value less than 6?
>* I don't know what values to specify for x for each give probability value.*
“x” in your code is in the place of the “nei” parameter, which specifies the
maximum distance within which two vertices will be connected in the initial
lattice from which the Watts-Strogatz model starts. Judging by the fact that
you specified dim=1 in the parameters, you want to start out from a ring graph.
In this case, if x=1, it means that each node will be connected to its nearest
neighbors in the ring only, and the rewiring (with the given probability)
starts from there. If x=2, if means that each node will be connected to its
nearest neighbors on the ring plus the next ones. In general, if you have a
ring with vertices 0, 1, 2, …, n-1, then vertex i will be connected to vertices
(i-x), (i-x+1), …, (i+x-1), (i+x), of course modulo n since this is a ring with
n nodes. (And of course vertex i will not be connected to itself).
Try plotting Graph.Watts_Strogatz(1, n, x, 0) for x=1, x=2, x=3 and so on,
with, say, n=15 to understand how the initial graph is generated and use the
“circle” layout (e.g, plot(Graph.Watts_Strogatz(1, 15, 2, 0), layout=“circle”)).
T.