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Given the interest in random nets, FWIW, I provide an early sociological
account of random and clustered networks in my

"Structural Analysis: From Method and Metaphor to Theory and Substance."
Pp. 19-61 in Social Structures: A Network Approach, edited by Barry
Wellman and S.D. Berkowitz. Cambridge: Cambridge University Press, 1988.

A scanned version is on my website.
 Barry
 _____________________________________________________________________

  Barry Wellman         Professor of Sociology        NetLab Director
  wellman at chass.utoronto.ca  http://www.chass.utoronto.ca/~wellman

  Centre for Urban & Community Studies          University of Toronto
  455 Spadina Avenue    Toronto Canada M5S 2G8    fax:+1-416-978-7162
             To network is to live; to live is to network
 _____________________________________________________________________

On Wed, 19 Nov 2003, David Lusseau wrote:

> Date: Wed, 19 Nov 2003 10:06:16 -0000
> From: David Lusseau <[log in to unmask]>
> To: [log in to unmask]
> Subject: Re: Random network generation
>
> *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****
>
> The fact that the random networks are composed of many isolates is an
> interesting fact in itself. If re-iterated many times, one could get the
> likelihood that, given the number of nodes and links observed in the
> real-world network, all nodes are connected in one giant cluster. If it is
> unlikely (observed once or twice over 100-1000 re-iterations or whatever
> level of significance one wants to choose) this tells us a lot about the
> real-world network: it is most likely not based on a random attachment
> mechanism.
>
> best,
> david
>
>
> David Lusseau
> Postdoctoral fellow
>
> University of Aberdeen
> Department of Zoology
> Lighthouse Field Station
> George St
> Cromarty
> Ross-shire IV11 8YJ
> Scotland
>
> Tel/Fax: 44 (0) 1381 600 548
>
> Lighthouse Field Station (University of Aberdeen):
> http://www.abdn.ac.uk/~nhi519/lighthse/index.hti
>
> New Zealand Whale and Dolphin Trust:
> http://nzwhaledolphintrust.tripod.com/home/
>
> Marine Mammal Research Group (University of Otago):
> http://www.otago.ac.nz/marinescience/mammals/home.htm
>
> Fiordland Research (University of Otago)
> http://www.otago.ac.nz/marinescience/fiords/home.htm
>
> ----- Original Message -----
> From: "Vaughan" <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Tuesday, November 18, 2003 11:03 AM
> Subject: Random network generation
>
>
> > *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****
> >
> > Hello everyone,
> >
> > I would like to generate a random network, with a similar number of ndoes
> > and connection to the network I have created from field data, to compare
> the
> > distance and clustering co-efficient of each. Not unlike the the method in
> > http://arxiv.org/pdf/cond-mat/0307439
> >
> > My network created from field data has no isolated nodes. However, when I
> > ask Pajek to create a network with the same number of nodes and
> connections
> > I get plenty of isolates, which apparently will not make a valid
> clustering
> > co-efficient or distance comparison.
> >
> > Andrew Shipilov kindly suggested to my that it is possible to generate
> > distance and clustering coefficients purely from knowing the number of
> nodes
> > and connections I wish to use, although I am having trouble tracking down
> > this method.
> >
> > Can anyone suggest a way of either generating a random network with a
> > specified number of nodes and connections that has no isolates or doing
> the
> > above calculation ?
> >
> > Many thanks,
> > Vaughan Bell
> >
> > _____________________________________________________________________
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> _____________________________________________________________________
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