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One further plea for recognition of previous work here.  The "preferential
attachment model" is what mathematical epidemiologists call "proportional
mixing".  It was the starting point for epidemic modeling in the mid
1980s.  Prior work had milked this assumption for all it was worth to get
analytical solutions to epidemic models.  But there was a small body of
work that began to hack away at the much harder problem of getting
solutions when mixing was not proportional.  Not much in the way of
analytic solutions was found, so most of the applied research used
simulation instead.

For the people working in this area, the idea of deriving the properties
of transmission systems under proportional mixing seems like a real blast
from the past.  Of course it can be done, it's just not clear why you
would want to.  At least, not if you were interested in understanding the
population dynamics of sexually transmitted infections.  In that context,
the assumption is just wrong, and it matters.

On Tue, 28 Jan 2003, Mark Newman wrote:

> *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****
>
> There are two issues here: one is failure to give credit where it's due
> and the other is the actual validity of the work.  I'm just finishing up
> a lengthy review article on recent work on networks by mathematicians
> and physicists, and although I thought I knew this literature quite well
> before I started, I have learned a lot by reading up for the review.  I
> agree completely that people have in some cases failed to give credit
> for earlier innovations, and this is bad.  But it would be a mistake to
> dismiss this work out of hand.  There is a great deal there that would
> be of interest to all of us.
>
> In particular response to Mark Handcock's post about "scale-free
> networks", I think it would certainly be a mistake to claim that the
> physics models, like the "preferential attachment" models, are complete
> models of the structure of networks.  Of course there are many different
> processes going on in network formation, most of which are absent from
> these models.  Therefore, if one compares these simple models to
> sociometric data, it's virtually certain they won't match up, and Mark's
> work demonstrates this elegantly.  This however doesn't make the models
> useless.  There's much to be learned from them, even if they are
> incomplete (or maybe even plain wrong).  At the very least, they've
> stirred up a whole new community to get interested in network ideas, and
> surely that can't be all bad.
>
> Mark Newman.
>
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****************************************************************
 Blumstein-Jordan Professor of Sociology and Statistics
 Department of Sociology
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 University of Washington
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