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Dear Enzo,
Dear Enzo,
Exactly right.  The infinite series that gives meaning to beta centrality does not converge if beta is greater than or equal to the inverse of the largest eigenvalue of the adjacency matrix.  


Phillip Bonacich
Professor Emeritus of Sociology
University of California, Los Angeles

-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On Behalf Of Vincenzo Nicosia
Sent: Monday, September 28, 2015 12:43 PM
To: [log in to unmask]
Subject: Re: Bonacich results negative...

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On Mon, Sep 28, 2015 at 03:21:31PM -0400, Jordi Comas wrote:

[cut]

>    So, can someone help me out?  To my eyes, the Bonacich algoritihim sums up
>    the centrality score of each node by weighting each node.  How can and
>    additive series get a negative score?
>    Thanks!
>    Jordi
>    (cookies in the mail for you for good answer.  :) )

The problem is that if \beta is larger than the inverse of the largest eigenvalue of the adjancency matrix, the sum which defines the centrality scores does not converge any more. One of the practical consequences is that the negative values will appear here and there in your eigenvector, but the basic message is that the results you get for your centrality scores loose any meaning.

My2Cents

Enzo

--
[ Enzo Nicosia - School of Mathematical Sciences - Queen Mary UL ] [ -- v.nicosia [at] qmul.ac.uk -- katolaz [at] yahoo [dot] it -- ] [ -- web @QMUL: http://maths.qmul.ac.uk/~vnicosia/index.html  -- ] [ twitter:@KatolaZ -- jabber:[log in to unmask] - skype: katolaz ]

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