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A couple of questions:

(1) what exactly is and is not new in the recent research in scale free
networks?  clearly, the importance of "hubs" has been known for a long
time, although the power law research clearly accents those findings.  As
the e-mails below discuss, there was some work on this going back on "scale
free" type ideas to at least the 1940s, and I've heard some allusions to
work going back to the 1920s.  exactly what was found, however, is still a
vague to me, and certainly had not been part of the core of social network
attention for a while.  Some other power law type research, e.g. city size,
earthquake distribution, war casualty distributions, etc, goes back many
decades, with spikes in attention with the work on "self-organized
criticality" in the 90s, and, before that, on firm size in the econ lit in
the 1950s and 60s.  (I also bet that number of responses to socnet e-mails
is power law distributed, most queries generating few responses, and a few,
such as this generating a large number.)

(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?

David



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                      .EDU                     Subject: Re: Erroneous facts / NyT article on social networks


                      01/26/2003 09:24
                      PM
                      Please respond
                      to buttsc






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Mark Newman wrote:
> And Rapoport touched on the same ideas even earlier in his work
> on friendship networks, although he didn't specifically discuss
> power-law degree sequences.
>

Indeed.  For that matter, there was a lot of very wonderful technical
work by physicists, biologists, and others on both social and biological
networks back in the late 1940s/early 1950s in the _Bulletin of
Mathematical Biophysics_ (of which Rapoport's work was part).  My sense
is that there is a fair amount of awareness of this literature within
the modern network community, but I'm not sure to what extent the
"scale-free" crowd is cognizant of it....

> Still, as David Gibson points out, one shouldn't blame Duncan Watts for
> this.  In fact, Duncan gives ample credit to the pioneers of the field
> in his new book.

I also noted that he was quoted as asking people to tone down the
hype....not that I expect the message to sink in.  Looks like we're in
for a bubble/crash cycle here -- I hope someone here is collecting data
on this!

-Carter

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