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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 22 187–220
ATA S.p.A Lucca Italy
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