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

Carl Nordlund wrote:

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> 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

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Thomas W. Valente, PhD
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