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SOCNET  May 2006

SOCNET May 2006

Subject:

Re: Network Homogeneity

From:

Erik Volz <[log in to unmask]>

Reply-To:

Erik Volz <[log in to unmask]>

Date:

Mon, 8 May 2006 00:24:47 -0400

Content-Type:

text/plain

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*****  To join INSNA, visit http://www.insna.org  *****

Tim, I would like to give another nod to MEJ Newman's paper. His measure is
quickly becoming the standard-- in three years his paper has been cited more
than 160 times. It's probably your best bet for what you want-- a  simple
metric describing the level of non-random mixing by type. Most of the other
papers concern statistical models of networks rather than descriptive
metrics. I suspect they would take you rather far afield.

Similar metrics been proposed in the epidemiology literature. The most
similar work in the Social Networks literature is by JS Coleman (1958
"Relational analysis...") who defined "homophily" as a measure of non-random
mixing ("a tendency to in-choice"). Identical metrics were proposed by
Rapoport around the same time. More recently Douglas Heckathorn has further
developed the idea of homophily.

Erik Volz

On 5/4/06, Mark S. Handcock <[log in to unmask]> wrote:
>
> *****  To join INSNA, visit http://www.insna.org  *****
>
> Tim,
>
> 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
> ways.
>
> 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,
> 12:156--192.
>
> 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!
>
> Regards,
>
> Mark
>
> -------------------------------------------------
> 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
> Web: www.stat.washington.edu/handcock
> 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:
> >
> >   http://arxiv.org/abs/cond-mat/0209450/
> >
> > There have certainly also been other earlier discussions of the issue,
> > particularly in the epidemiology literature, some of which are cited
> > in the above.
> >
> > Mark
> >
> >
> >
> > 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
> >
> > _____________________________________________________________________
> > SOCNET is a service of INSNA, the professional association for social
> > network researchers (http://www.insna.org). To unsubscribe, send an
> > email message to [log in to unmask] containing the line
> > UNSUBSCRIBE SOCNET in the body of the message.
>
> _____________________________________________________________________
> SOCNET is a service of INSNA, the professional association for social
> network researchers (http://www.insna.org). To unsubscribe, send
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>

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