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## Re: [igraph] How to Generate scale-free network with the vertex's in-deg

 From: Gábor Csárdi Subject: Re: [igraph] How to Generate scale-free network with the vertex's in-degree and out-degree negatively correlated Date: Fri, 4 Apr 2014 07:37:44 -0400

On Thu, Apr 3, 2014 at 8:52 PM, address@hidden wrote:
Hi

I am sorry that I did not put the question clear.

The correlation between in-degree and out-degree is different from the assortativity coefficient.
The former one can be exsit in any type of directed graph but the latter one are only in scale-free graph.
Why?
When we regard the in-degree and out-degree of a vertex as two random variables j and k,
if P(j, k) = P(j) * P(k), where P(j) means the probability of indegree=j, then there is no correlation between in-degree and out-degree.
if P(j, k) != P(j) * P(k), then in-degree and out-degree are correlated.

I want to generate ER graphs and scale-free graphs with the in-degree and out-degree correlated.
Is there any functions can do these?
Yes, just generate your in-degree and out-degree sequences any way you like, and then use degree.sequence.game.

Gabor

best
Xueming

Date: 2014-04-03 21:01
Subject: Re: [igraph] How to Generate scale-free network with the vertex's in-degree and out-degree negatively correlated
Well, that's a little loosely defined. Maybe you want to sample networks while conditioning on the degree distributions (or degree sequences) and the assortativity coefficient. I am not sure how to do that, but there might be some papers about it. I would search for 'generate networks assortativity degree distribution': https://www.google.com/search?q=generate+networks+assortativity+degree+distribution

Gabor

On Thu, Apr 3, 2014 at 4:28 AM, address@hidden wrote:
Hi,

I want to generate directed scale-free networks.
The in-degrees and out-degrees of vertex are negatively correlated.
Which command could I use to generate such scale-free networks?

best
Xueming

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