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

 

The (degree) distribution underlying the figure depicted in Barabasi's
article (the one Valdis drew our attention to) follows a "scale free" (or
power law) distribution. I've found that the degree distributions in the
organizational samples I've collected more closely resemble the normal
distribution; but the distribution of betweenness centrality does resemble
the power law distribution that Barabasi, Watts and others have found
(across a remarkable range of networks, from the nervous system of
one-millimeter worm C. Elegans to the electricity network of the Western
United States). Also, in the organizational samples I’ve examined, the
distribution of degree centrality in certain types of networks (e.g.,
“perceived leadership” network) follow the power law distribution, but the
distribution of degree centrality in other networks (e.g., the trust
network) does not.

 

To understand why “human” networks may in some cases follow scale free
distributions and normal distributions in others will probably require close
attention to the theoretical logic that is used to explain the dynamic
growth (and decay) of these networks. Barabasi and colleagues have focused
on “growth” (the periodic addition of nodes to a network over time, starting
with the nucleus) and “preferential attachment” (the idea that new nodes
prefer to connect with nodes that have more ties rather than with nodes with
fewer ties) as the twin engines of network dynamism. These principles make
sense in many systems. But they surely don’t hold for all systems: In
friendship networks, for example, nodes may prefer to connect with similarly
connected nodes rather than with the best connected ones. Not everyone
reaches out to the stars.

 

One reason that physicists like Barabasi are so excited about the “new”
science of networks is that it holds out the promise for general laws of
networks that would apply across all kinds of networks. Those studying
organizational networks have argued for some time that this quest for
general laws may be misguided. Still, I for one say let’s not dampen the
physicists enthusiasm just yet. Even if their quest for universal laws of
networks proves unattainable, they are sure to throw up marvelous insights
along the way.

 

Ajay Mehra

University of Cincinnati

 

    

 

 

 

 

 

 

 

-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
Behalf Of Steven Corman
Sent: Wednesday, February 02, 2005 10:22 AM
To: [log in to unmask]
Subject: Re: All Networks Look the Same?

 

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

 

Three thoughts...

 

(1) These (valid) critiques notwithstanding, let us acknowledge that it is
interesting if there is some kind of fractal quality to large networks.

 

(2) One wonders what characteristic might distinguish networks that are
self-similar from those that aren't. Is it social vs. physical networks as
Tom implies? Or a function of size as Bettina suggests? If size, what's
the tipping point?

 

(3) INSNA members seem not to be part of the networks of paper reviewers and
science reporters who are creating this "new" science of networks. Why is
that?

 

Best,

 

Steve

 

________________________________________________

Steven R. (Steve) Corman

Professor, Hugh Downs School of Human Communication

Arizona State University

http://www.public.asu.edu/~corman

 

Chair, Organizational Communication Division

International Communication Association

http://www.icahdq.org

 

 

-----Original Message-----

From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
Behalf Of Bettina Hoser

Sent: Wednesday, February 02, 2005 7:09 AM

To: [log in to unmask]

Subject: Re: [SOCNET] All Networks Look the Same?

 

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

 

Hi

This self-similarity idea has been around as it seems for a while. I just
checked my own (limited) literature base and found an article from 2002
http://arxiv.org/pdf/cond-mat/0211498 which was released in Physical Reveiw
letter E.

 

As of now I do not have hands-on experience if this is really true, but it´s
not a new idea.

 

But just as a philosophical thought: once the network - any network - gets
big enough isn´t it somehow quite likely to become self-similar?

 

Best regards,

Bettina

 

--

Dipl.-Phys. Bettina Hoser

Informationsdienste und elektronische Märkte

Fakultät für Wirtschaftswissenschaften

Universität Karlsruhe (TH)

D-76128 Karlsruhe

 

Gebäude 20.20 RZ (Raum 164), Zirkel 2

 

Telefon: +49.721.608-8407

Telefax: +49.721.608-8403

 

[log in to unmask]

http://www.em.uni-karlsruhe.de

 

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