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Thomas,

The paper you mention on the arxiv appears to be about the joint 
degree-degree distribution in a single network.  There are quite a few 
papers on that.  For example, one can have an ensemble of random graphs 
in which one fixes not only degree distribution but also the joint 
degree-degree distribution.

What you're trying to study appears to be about degree distributions of 
different kinds either in different networks or in different types of 
edges in a multiplex network.

This is not quite the same mathematical object (even before one computes 
something like a Pearson coefficient).  In the former, a Pearson 
coefficient would summarize the properties of the full joint distribution, 
so it really depends on whether you only care about such a summary or want 
more information.  (You might find it useful to look up assortativity by 
degree, though given that your actual object of study is somewhat 
different, this is somewhat different from what you're really looking at 
anyway.  You could define something similar in your situation if you 
wanted to.)

-----
Mason





>
> Date:    Fri, 27 Jan 2012 18:15:18 +0100
> From:    Thomas Plotkowiak <[log in to unmask]>
> Subject: Correlation of degree distributions
>
> --f46d040f9ca21336ca04b785a415
> Content-Type: text/plain; charset=ISO-8859-1
>
> *****  To join INSNA, visit http://www.insna.org  *****
>
> Since degrees distributions in networks are heavy tailed and are thus not
> normally distributed and is it still ok to correlate them using some
> correlation measure like pearsons r? Is it robust enough?
>
> Lets say we have a network that notes friendships, and a network that notes
> the actually exchanged information. So a hypothesis could be that persons
> with a high amount of friends also exchange a lot of information. For that
> I would correlate the degrees of those two networks. Would that be a valid
> approach?
>
> P.S.
> I've found a paper on arxiv on this, maybe you know of more:
> http://arxiv.org/pdf/1003.1634.pdf
> I also remember hearing something about the QAP correlation (
> http://faculty.ucr.edu/~hanneman/nettext/C18_Statistics.html) method, but i
> think it was for the case when both network measures come from the same
> network.
>



-----
Mason

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  Mason A. Porter
  University Lecturer (and Tutorial Fellow, Somerville College)
  Oxford Centre for Industrial and Applied Mathematics
  Mathematical Institute, University of Oxford

  Homepage: http://www.maths.ox.ac.uk/~porterm, IM: tepid451
  Blog: http://masonporter.blogspot.com/
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  "That's my new excuse, and I'm sticking to it." (Me)
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