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One small correction -- since this discussion is now being preserved
for posterity.

Mark Newman pointed out that I was not entirely correct in saying that
preferential attachment models are the same as proportional mixing models.

He's right, of course. Preferential attachment is an unconditional
dynamic model of link formation, and prop mixing is conditional on a fixed
degree distribution. They have very different implications for degree
distributions.

My comments were focused on the common component of the two models, the
assumption of random mixing by degree. Relaxing the random mixing
assumption has been the focus of most epi modeling for the last 15 years.

With respect to mixing by degree, the empirical motivation is fairly
obvious: consider polygamy (disassortative by degree) and bath houses
(assortative by degree). The impact this has on transmission dynamics is
also clear -- disassortaive creates slower growing, more widespread
epidemics, while assortative creates rapid but contained spread.

These are the implications of networks that matter for public health.
They are driven by data, and modeled accordingly.


****************************************************************
 Blumstein-Jordan Professor of Sociology and Statistics
 Department of Sociology
 Box 353340
 University of Washington
 Seattle, WA 98195-3340

Phone Numbers:
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 Dept Office: (206) 543-5882
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