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That is the correct answer. Eigenvector will always assign a zero to the
smaller components and so should not be used on graphs with more
than one component.

You could look at the components separately, but this means you
cannot compare centralities across components.


On 8 Mar 2005 at 8:28, Skye Bender-Demoll wrote:

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>
> Hi all,
>
> Does anybody have any experience with / references for eigenvalue
> centrality measures and graphs with multiple components?
>
>   We are starting to work with the standard eigenvector centrality
>   measure,
> but the networks we use contain multiple components.  Not
> surprisingly, this seems to cause some problems.  The eigenvector
> calculation (both in UCINET and in matlab) gives correct results for
> the largest components, but zero for all the other components.  When
> we run the calculation on one component alone, we get very different
> results.  I'm guessing that the eigenvector centrality measure is not
> defined for multiple components? (UCINET seems to suggest this)
>
> Or are the values for the smaller component (a three node chain in a
> test example) so small when compared with the large component (a 5
> node bow-tie) that they are lost in round off during the eigenvector
> calculation?
>
> If we run the algorithm independently on each component, can we
> compare scores between components, or are they only valid within
> components?  (I'm assuming that in the UCINET-style version where the
> scores are normalized they should only be compared within components?)
>
> Any suggestions welcome ( I have yet to locate many papers directly
> related to this, nor in the socnet archives)
>
> 1)  R. Poulin, M.-C. Boily  B.R. Masse (2000) "Dynamical systems to
> define centrality in social networks" Social Networks 22 187220
>
> thanks,
>    -skye
> ATA S.p.A Lucca Italy
>
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