[statnet_help] Inquiry about eigenvector centrality normalization in sna package

[CHU-DING LING via statnet_help]

Dear Carter,



Thank you for your detailed explanation regarding the normalization of
eigenvector centrality scores in the *sna* package. Your guidance will
certainly help me and others in the community achieve greater clarity in
using these tools. Thank you again for your valuable input.



Best regards,

Chuding


Carter T. Butts via statnet_help <statnet_help at u.washington.edu>
于2024年9月8日周日 17:12写道：


> 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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