Dear Dorothea,
I don't know which version of UCINET you used. I tried the BURT-Data in
UCINET V and in an old DOS-Version distributed free on the analytic
technologies homepage and both versions gave the correct result of 16 for
the non-normalised betweenness. According to the UCINET manual the routine
is based on Freeman (1979).
The UCINET manual says:
Let bjk be the proportion of all geodesics linking vertex j and vertex k
which pass through vertex i. The betweenness of vertex i is the sum of all
bjk where i, j and k are distinct and j < k. Betweenness is therefore a
measure of the number of times a vertex occurs on a geodesic. The
normalised betweenness centrality is the betweenness divided by the maximum
possible betweenness expressed as a percentage.
This procedure should only sum over every pair once, because of the j<k, but
for asymmetric data the routine sums over all ordered pairs j,k where i, j
and k are distinct. Details can be found in Gould (1987). Of course by
taking every ordered pair instead of every pair the number of pairs and thus
the maximum possible betweeness is also doubled. So, for normalisation
purposes the denominator has to be doubled, too.
Freeman L C (1979). 'Centrality in social networks: Conceptual
clarification'. Social Networks 1, 215-239.
Gould R V (1987). 'Measures of betweenness in non-symmetric networks'.
Social Networks 9, 277-282
I hope this helps
Mark
At 20:07 07.08.2002 +0200, you wrote:
>Hi all,
>
>UCINET does calculate betweenness for asymmetric data, but I can't find
>out which routine is used. Playing with a very simple graph, the advice
>net of Burt (1982: 25), UCI yields betweenness scores of zero for all
>actors, although actor 5 is the only go-between on 16 geodesics of
>length 2 which are correctly identified. Is there a threshold of
>connectedness for the calculation routine used?
>The advice networks consists of 10 nodes which can be grouped to four
>perfect blocks. 1 to 4 only have an outgoing tie to 5. Actor 6 is
>unconnected. 5 has outgoing ties to 7 to 10. 7 to 10 are a perfect
>clique.
>Thank you for any help
>
>Dorothea
>
>
>--
>Prof. Dr. Dorothea Jansen
>Lehrstuhl für Soziologie der Organisation
>Deutsche Hochschule für Verwaltungswissenschaften
>Postfach 1409
>D-67324 Speyer
>
>Tel. 06232/654-364 oder -359 (Sekretariat)
>Fax: 06232/654-418 oder -306
>Homepage: http://www.dhv-speyer.de/jansen/
>
-----------------------------
Mark Trappmann
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http://www.fb1.uni-essen.de/trappmann
Telefon ++49 (0)201-183-2586 (Uni Essen)
(0)203-663944 (Duisburg)
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