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On Nov 16, 2003, at 2:26 PM, Vaughan wrote:

> I would like to find out whether the network I have is a small world or
> scale free network (or neither), however it is not obvious to me which
> analysis in any of these software packages would tell me this.
> I have a background in psychology, rather than graph theory or
> sociology so
> some of the literature is a little mysterious to me. I have papers
> which
> define small world / scale free networks in mathematical terms but no
> pointers as to how (and if) this is implemented in relevant software
> packages.

I know of no software packages that implement what you're looking for.
JUNG (of which I am one of the developers) can generate small-world
networks, but it does not, as yet, include mechanisms to evaluate how
closely a given network resembles a small-world network.

(In a sense, the question "is this a small-world network?" is not
well-posed, because "small-world network" is a description of a
statistical property; it's exactly analogous to asking whether data is
normally distributed.)

I assume that the question you'd really like to be able to ask is "how
similar is the distribution of properties (e.g., degree) of this
network similar to that of a small-world network?", and/or "what is the
small-world network which is most similar to this network?", and
similarly for scale-free networks.  I don't know of a clean way to
evaluate this; the general strategy that I would use would be to
calculate the properties (e.g., degree distribution) for my network,
and then find (via something like binary search on the generative
parameter(s)) the small-world graph whose distribution most closely
resembles that of your network.  Then you can decide whether the match
is close enough for your purposes.

Hope this helps.  If you'd like some assistance in implementing the
scheme mentioned above in the JUNG framework (which can read basic
Pajek .net files), please feel free to contact me.


Joshua O'Madadhain Per
   Joshua O'Madadhain: Information Scientist, Musician,
  It's that moment of dawning comprehension that I live for--Bill
My opinions are too rational and insightful to be those of any

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