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I would reinforce Martina's point in a little less polite way: the idea
that human interaction networks might be scale-free [as opposed to other
systems of orientation among human beings, which can transcend physical
and technological limits: e.g,. the worldwide network of "fame"
attributions may be scale-free] is obviously wrong and reflects the
larger mistake of blindly applying the same principles both to physical
and social systems.

Another thought for this string: if anyone out there doesn't believe in
the Matthew Effect, they certainly have ample proof from the furor over
the small world and scale-free networks.  To the extent that physicists
are credited with having invented network analysis, it tells you more
about the reproduction of status hierarchies than anything else.  And to
the extent that this bothers us, it tells us how inescapable status
hierarchies are.

Ezra W. Zuckerman
MIT Sloan School of Management
50 Memorial Drive, E52-564
Cambridge MA 02142
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Tel: 617-253-1918
Fax: 617-253-2660


-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
Behalf Of Martina Morris
Sent: Monday, January 27, 2003 1:30 PM
To: [log in to unmask]
Subject: Re: Erroneous facts / NyT article on social networks

*****  To join INSNA, visit http://www.sfu.ca/~insna/  *****

On Mon, 27 Jan 2003, David Lazer wrote:


> (2) what networks tend to be scale free, and what networks not?  The
> interpersonal data I tend to work with I'm pretty sure tend to be
normally
> distributed.  Many other kinds of networks, as Barabasi and others
have
> shown, are power law distributed in in-degree.  If one were to survey
> social network data sets, and categorize them by type of distribution
of
> in-degree, what would the categories be, and what would be the
variables
> underlying those categories?  Has this been done?


To do this, you would really need a principled statistical method for
comparing an observed distribution to any number of alternative
distributions, and for estimating the parameters of the distributions
from
data.  The much cited Nature paper used simple linear regression, which
is
completely inappropriate.  Nothing of this sort has been published yet,
but a paper is under review (and getting savaged by the same folks who
think that statisticians only know about normal distributions).

Intuitively, though, the scale free property implies tail behavior that
is
physically impossible in social contact networks.  Indeed, it implies
that
there is a small, but non-zero, probability that someone can have more
contacts than there are members of the population.  And this property
underlies many of the "newsworthy" analytic results that follow -- i.e.,
that there can be no effective interventions for sexually transmitted
diseases.


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

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