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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.


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