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Hi Zachary

An interesting question.  

I mentally conceptualise Bonacich power as beta loading the impact of second degree effects.   I would suggest a further dimension to the conundrum of interpreting Bonacich power, that is under what assumptions you would select a negative beta.  Since the algorithm imputes centrality by weighting the centrality of alters and since centrality is often associated with power, it is an issue of theoretical relevance whether one should be considered more or less 'powerful' as a result of the centrality of their alters, ceteris paribus.  

In political networks an actor connected to highly central others can exercise influence or alternatively by being connected to less central others they can exercise dominance /control. A positive beta augments and a negative detracts from the effect of alters centrality on an actor's own centrality.  The choice of a negative beta in this context could imply that one distinguishes between influence ties and dominance ties.

And of course as has been stated before, negative coefficients cannot be interpreted as lower than positive ones.      

My two (fast devaluing) Euro cents

Dimitris

Dr Dimitris Christopoulos

Award Leader,
MA Applied Social Research

Editor, Connections
www.insna.org/pubs/connections

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Department of Politics
UWE-Bristol
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-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On Behalf Of Zachary P Neal
Sent: 09 December 2011 14:27
To: [log in to unmask]
Subject: Interpreting negative values of Bonacich Centrality

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When computing Bonacich centrality with a negative beta, the resulting  
scores can include both positive and negative values.  This can occur  
even when the magnitude of beta is less than 1/largest eigenvalue.

In past Socnet posts and in the existing literature, there seems to be  
some disagreement about how to interpret the negative values.  Some  
suggest that negative values should be interpreted directly, as  
reflecting lower centralities than the positive values.  Others have  
suggested that the +/- signs are not meaningful, and that one should  
interpret only the scores' absolute value.  In a 2008 Socnet post,  
Martin Everett offered still a third suggestion: set the magnitude of  
beta small enough that the measure does not produce any negative scores.

Which is the correct approach?  Is there an authoritative published  
reference for this issue?

Thanks,
Zachary

-- 
Zachary Neal, Assistant Professor
Michigan State University
Department of Sociology & Global Urban Studies Program
316 Berkey Hall
East Lansing, MI 48824
http://www.msu.edu/~zpneal

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