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Friedkin defined the unique in and out degree nodes as distinct points.
-Tom

Carl Nordlund wrote:

> *****  To join INSNA, visit http://www.insna.org  *****
>
> Hi SocNetters,
>
> I have a question on a centrality index - don't know if I just
> invented a new one, or whether I have reinvented an old wheel of
> unknown quality...
>
> In my PhD thesis, I play around with intl trade flow matrices, i.e.
> directional valued matrices with quite large value-spans between
> different actors. While primarily looking at the role-structures
> (conceptualized through regular equivalence), I am also interested in
> looking at the relationship between different indices of "centrality"
> and more mainstream (actor-based) attributes on economic well-being.
>
> As I am especially interested in the number of trading partners each
> country has, both with regards to exports and imports, I have
> experimented with a simple heuristic for counting the number of
> significant trading partners for each country. However, I don't know
> if this same procedure has been done before - and if so, what this
> type of degree-style centrality index is called.
>
> How I calculate the number of partners an actor has:
> First, I look at the "outflow profile", i.e. the row-vector for each
> actor. Each outflow that is larger than 0.5 percent of the total
> outflow is included in my count. I.e., if an actor has a total
> outdegree of 1000, I count the number of outflows which are higher
> than 5. Secondly, I do the same thing for the "inflow profile", i.e.
> by looking at the col-vector for each actor. Similarly, I count all
> inflows that are above 0.5 percent of the total inflows to the actor.
> Then I calculate total number of partners by adding the number of
> inbound and outbound partners. (The 0.5 percent "significance
> threshold" is of course arbitrary). (As the same partner actor could
> be counted twice - inbound as well as outbound - one could choose to
> only count each trading partner once).
>
> What I thus try to do is to only count the number of "significant"
> partners, where significance is defined on a per-actor basis. The
> resulting index is very interesting for my data-set: I find a
> statistical association between total number of trading partners
> (weighted to total trade flows) and economic well-being.
>
> What is this centrality index called (as I assume the above has been
> done before)?
>
> Yours,
> Carl
>

--
http://www.oup-usa.org/isbn/0195141768.html
My personal webpage:
http://www-hsc.usc.edu/~tvalente/
---
Thomas W. Valente, PhD
Director, Master of Public Health Program
http://www.usc.edu/medicine/mph/
Department of  Preventive Medicine
School of Medicine
University of Southern California
1000 S. Fremont Ave.
Building A Room 5133
Alhambra CA 91803
phone: (626) 457-6678
fax: (626) 457-6699