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Brain network analysis : separating cost from topology using costintegration
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Ginestet, Cedric E., Nichols, Thomas E., Bullmore, Edward T. and Simmons, Andrew. (2011) Brain network analysis : separating cost from topology using costintegration. PLoS ONE, Vol.6 (No.7). Article: e21570. ISSN 19326203

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Official URL: http://dx.doi.org/10.1371/journal.pone.0021570
Abstract
A statistically principled way of conducting brain network analysis is still lacking. Comparison of different populations of
brain networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the number of
edges in an unweighted graph. In this paper, we evaluate the benefits and limitations associated with using costintegrated
topological metrics. Our focus is on comparing populations of weighted undirected graphs that differ in mean association
weight, using global efficiency. Our key result shows that integrating over cost is equivalent to controlling for any
monotonic transformation of the weight set of a weighted graph. That is, when integrating over cost, we eliminate the
differences in topology that may be due to a monotonic transformation of the weight set. Our result holds for any
unweighted topological measure, and for any choice of distribution over cost levels. Costintegration is therefore helpful in
disentangling differences in cost from differences in topology. By contrast, we show that the use of the weighted version of
a topological metric is generally not a valid approach to this problem. Indeed, we prove that, under weak conditions, the
use of the weighted version of global efficiency is equivalent to simply comparing weighted costs. Thus, we recommend the
reporting of (i) differences in weighted costs and (ii) differences in costintegrated topological measures with respect to
different distributions over the cost domain. We demonstrate the application of these techniques in a reanalysis of an fMRI
working memory task. We also provide a Monte Carlo method for approximating costintegrated topological measures.
Finally, we discuss the limitations of integrating topology over cost, which may pose problems when some weights are zero,
when multiplicities exist in the ranks of the weights, and when one expects subtle costdependent topological differences,
which could be masked by costintegration.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry T Technology > TK Electrical engineering. Electronics Nuclear engineering 

Divisions:  Faculty of Science > Statistics Faculty of Science > WMG (Formerly the Warwick Manufacturing Group) 

Library of Congress Subject Headings (LCSH):  Graph theory, System analysis, Brain  Mathematical models  
Journal or Publication Title:  PLoS ONE  
Publisher:  Public Library of Science  
ISSN:  19326203  
Official Date:  28 July 2011  
Dates: 


Volume:  Vol.6  
Number:  No.7  
Number of Pages:  17  
Page Range:  Article: e21570  
Identifier:  10.1371/journal.pone.0021570  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Open Access  
Funder:  National Institute for Health Research (Great Britain) (NIHR), Guy's & St. Thomas' Hospital Trust. Charitable Foundation, South London and Maudsley NHS Trust  
References:  1. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘smallworld’ networks. 

URI:  http://wrap.warwick.ac.uk/id/eprint/36875 
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