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Hey All,

I am working on my dissertation in social psychology, and in the course
of reading Baker and Faulkner (1993), I suspect an error in computation
of graph closeness centralization. Their actor closeness (Eq. 3, p. 848)
  they call "farness" and later refer to it in note 8 as Sabidussi's
index. Wasserman and Faust (1994, p. 184) indicate that Sabidussi's
index is actually the reciprocal of this value. Further, their equation
is not standardized by multiplying by g - 1 (Wasserman &  Faust, Eq.
5.8), causing a problem for comparing across networks of different size.

One of their hypotheses was that the network with high information
processing (turbines conspiracy) should have the lowest graph
centralization, which I understand. They give Freeman's equation in
their Equation 4, but they compute closeness graph centralization using
their farness index rather than the standardized closeness index. I
interpret their number as unstandardized graph decentralization, but
they interpret it as regular centralization. In Table 1, they give
"Sabidussi graph centralization (farness)" numbers, and the turbines
network has the highest value. They conclude, "This illegal network
should be sparse and decentralized. This expectation is not supported by
the data. The turbines conspiracy network exhibits the highest density
and is the most centralized" (Baker & Faulkner, p. 850).

Am I correct in reinterpreting their number as unstandardized graph
decentralization? If so, am I correct in surmising that their conclusion
is backwards? If this is the case, is there a way to take their number
and the network size and algebraically obtain proper graph centralization?

I am rather confused by this and would greatly appreciate any advice you
can offer.

David M. Ouellette
Psychology Department, Social Division
Virginia Commonwealth University

References

Baker, W. E., & Faulkner, R. R. (1993). The social organization of
conspiracy: Illegal networks in the heavy electrical equipment industry.
American Sociological Review, 58, 837-860.

Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and
applications. Cambridge: Cambridge University Press.

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