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For network centralization as measured by the variance of the degrees, I 
have the old but still fresh paper:

Snijders, T.A.B., The degree variance: an index of graph heterogeneity.
Social Networks, 3 (1981), 163-174.
Abstract.
In the analysis of empirically found graphs, the variance of the degrees 
can be used as a measure for the heterogeneity of (the points in) the 
graph. For several types of graphs, the maximum value of the degree 
variance is given, and the mean and variance of the degree variance 
under a simple stochastic null model are computed. These are used to 
produce normalized versions of the degree variance, which can be used as 
heterogeneity indices of graphs.

This treats the relation between degree variance, density, and number of 
nodes; not with clustering if this is defined as transitivity. The 
maximum centralization as defined by maximum degree variance for given 
number of nodes and density is attained by highly transitive networks, 
however: either a network consisting of one clique with the rest 
isolates, or a core-periphery structure where the core is a clique.

Best,
Tom Snijders


Corey Phelps wrote:
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> Sender:       Social Networks Discussion Forum <[log in to unmask]>
> Poster:       Corey Phelps <[log in to unmask]>
> Subject:      clustering (coefficient), network density & centralization
> -------------------------------------------------------------------------------
> 
> *****  To join INSNA, visit http://www.insna.org  *****
> 
> I am looking for literature that discusses the possible relationship among
> clustering, network density and centralization (any measure of
> centralization). Work which provides empirical correlations among these
> variables would also be welcome. 
>  
> Thanks in advance.
>  
> Corey
>  
> Corey Phelps
> Asst. Professor, Management & Organization
> University of Washington
> Box 353200
> Seattle, WA  98195
> (206)543-6579
> [log in to unmask]
>   
> 
> 
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-- 
Tom A.B. Snijders
Professor of Statistics and Methodology
Scientific Director, ICS
Department of Sociology, University of Groningen
Grote Rozenstraat 31
9712 TG Groningen
The Netherlands
+31-(0)50-3636188/6216
http://stat.gamma.rug.nl/snijders/
Note: new email address: [log in to unmask]

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