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To add a bit of a historical perspective, these concepts have been studied almost as long as social network analysis has been.
Standard references and developments can be found in Breiger (1979), the discussion of Holland and Leinhardt (1981), Fienberg and
Wasserman (1981). A good review of this work (with references) is in text book Wasserman and Faust (1994) (Section 15.2 and Chapter
16). McPherson, Smith-Lovin, and Cook (2001) have a nice review of the central concept of homophily .
Martina Morris picked up on this in the early '90s, by which time the terms attribute/assortative/selective mixing were in common
use. Her papers discuss and develop many of the issues in network mixing.
There has been much recent development on the issue with degree correlation mixing being part of the ERGM framework and latent class
modeling building on the earlier block modeling (Nowicki and Snijders 2001 and the cites therein).
I do not think that these references or history appear in Mark's paper as he may not have been aware of them or that the ideas and
terms may have been in common usage (Google is your friend!). It would be good to cite the original sources, though, as cites to
Mark's paper alone disconnect from the established literature. Mark's paper does contribute to the discussion of mixing in other
Here are some of the references:
Breiger, R. (1979). Toward an operational theory of community elite structure, Quality and Quantity, 13, 21-47.
Fienberg, S. E. and Wasserman, S. (1981). Categorical Data Analysis of Single Sociometric Relations. Sociological Methodology,
Holland, P. W. and Leinhardt, S. (1981). An Exponential Family of Probability Distributions for Directed Graphs (with Discussion).
Journal of the American Statistical Association, 76(373):33--50.
Morris, M. (1991). A log-linear modeling framework for selective mixing. Mathematical Biosciences, 107, 349-377.
McPherson, M., L. Smith-Lovin, and J. M. Cook (2001). Birds of a feather: Homophily in social
networks. Annual Review of Sociology 27, 415-444.
Nowicki, Krzysztof, and Snijders, Tom A.B, Estimation and prediction for stochastic blockstructures.
Journal of the American Statistical Association, 96 (2001), 1077-1087.
I hope this helps!
Mark S. Handcock
Professor of Statistics and Sociology
Department of Statistics, C014-B Padelford Hall
University of Washington, Box 354322 Phone: (206) 221-6930
Seattle, WA 98195-4322. FAX: (206) 685-7419
internet: [log in to unmask]
----Original Message from Social Networks Discussion Forum <> on Tuesday, May 02, 2006 6:08 AM:
> ***** To join INSNA, visit http://www.insna.org *****
> At the risk of tooting my own horn, let me draw your attention to the
> following paper, where this question is discussed:
> Mixing patterns in networks, M. E. J. Newman, Phys. Rev. E 67,
> 026126 (2003).
> You can also find a copy here:
> There have certainly also been other earlier discussions of the issue,
> particularly in the epidemiology literature, some of which are cited
> in the above.
> On Tuesday 02 May 2006 05:02, Dr. Timothy R. Huerta wrote:
>> ***** To join INSNA, visit http://www.insna.org *****
>> Hello all!
>> Great Sunbelt. Nice seeing a bunch of you.
>> I was wondering if there was a metric that one could use to express
>> the degree to which relationships among categories of nodes are
>> equally distributed. For example, I have a network of 12 people, 4
>> short, 4 medium and 4 tall. I want to know if participants in the
>> network discriminate in the creation of ties by category.
>> I have an idea in mind, but I don't want to reinvent the wheel here.
>> Tim Huerta
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