[statnet_help] Inquiry about eigenvector centrality normalization in sna package

[Carter T. Butts via statnet_help]

Hi, Chuding -

Eigenvectors (and hence eigenvector centrality) are defined only up to a 
nonzero scalar multiple, so their lengths are inherently arbitrary;  
evcent() follows the behavior of eigen(), which in turn follows the very 
common convention of taking eigenvectors to be of unit length.  If 
rescale=TRUE, then the scores are rescaled so that the sum of scores is 
1 (which does not, in general, yield a unit-length vector).  However, 
this is again cosmetic, and you can make them sum to 5, to π, or to your 
birthdate if you like, without changing the meaning of the index.  (You 
can also flip their signs, if you like.  And, indeed, eigen()-based 
calculation can give you negative-sign solutions.  An all-negative 
solution is equivalent to an all-positive solution, because only the 
products of values matter.)

Hope that helps,

-Carter

On 9/7/24 9:32 PM, CHU-DING LING via statnet_help wrote:

>

> Dear Carter and all,

>

> I hope this email finds you well. I'm writing to discuss the 

> normalization of eigenvector centrality scores in the *sna* package.

>

> After reviewing the documentation, I saw that when ‘rescale=TRUE’ is 

> used, the 1-norm is applied for normalization. However, for the 

> default setting of ‘rescale=FALSE’, the documentation does not specify 

> the normalization method.

>

> Since the choice of normalization method can significantly affect 

> centralization calculations based on eigenvector centrality, I believe 

> it would be helpful to clarify this in the documentation. Is the 

> Euclidean norm used when ‘rescale=FALSE’, or could this be a side 

> effect of the eigenvector computation method?

>

> For reference, there is an ongoing discussion on this topic in the 

> following thread: 

> [https://igraph.discourse.group/t/clarification-on-eigenvector-centralization-calculation-in-igraph/1867/2 

> <https://urldefense.com/v3/__https://igraph.discourse.group/t/clarification-on-eigenvector-centralization-calculation-in-igraph/1867/2__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Mag52IdlUKL5O9HWcQYJP4oMfX-Js9neFXT7Jdz8RIxMCKyL76a1SpKv8BVmUr3yOn4Dltz1uEgzqsU2_RrnVIWs42mV$>]. 

> Your insights would be greatly appreciated and could help improve 

> consistency and clarity in network analysis tools across the R ecosystem.

>

> Thank you for your time and consideration.

>

> Best regards,

>

> Chuding

>

>

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