Shapley ratings in brain networks
Recent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the appli...
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2007-11-01
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doaj-f962700c2978445db9f338074e003f0d2020-11-24T22:53:47ZengFrontiers Media S.A.Frontiers in Neuroinformatics1662-51962007-11-01110.3389/neuro.11.002.200794Shapley ratings in brain networksRolf Kötter0Rolf Kötter1Rolf Kötter2Andrew T Reid3Andrew T Reid4Antje Krumnack5Egon Wanke6Olaf Sporns7Department of Cognitive Neuroscience, Radboud University Nijmegen Medical CentreInstitute of Anatomy II, Heinrich Heine UniversityVogt Brain Research Institute, Heinrich Heine UniversityDepartment of Cognitive Neuroscience, Radboud University Nijmegen Medical CentreVogt Brain Research Institute, Heinrich Heine University Department of Computer Science, Heinrich Heine University Department of Computer Science, Heinrich Heine UniversityDepartment of Psychological and Brain Sciences, Indiana UniversityRecent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the application of graph theoretical concepts to the analysis of these structures within their large-scale connectivity networks. In this paper, we explore the application of concepts from graph and game theory toward this end. Specifically, we utilize the Shapley value principle, which assigns a rank to players in a coalition based upon their individual contributions to the collective profit of that coalition, to assess the contributions of individual brain structures to the graph derived from the global connectivity network. We report Shapley values for variations of a prefrontal network, as well as for a visual cortical network, which had both been extensively investigated previously. This analysis highlights particular nodes as strong or weak contributors to global connectivity. To understand the nature of their contribution, we compare the Shapley values obtained from these networks and appropriate controls to other previously described nodal measures of structural connectivity. We find a strong correlation between Shapley values and both betweenness centrality and connection density. Moreover, a stepwise multiple linear regression analysis indicates that approximately 79% of the variance in Shapley values obtained from random networks can be explained by betweenness centrality alone. Finally, we investigate the effects of local lesions on the Shapley ratings, showing that the present networks have an immense structural resistance to degradation. We discuss our results highlighting the use of such measures for characterizing the organization and functional role of brain networks.http://journal.frontiersin.org/Journal/10.3389/neuro.11.002.2007/fullsulcal lengthconnectivityGame theorygraph analysisNeural Network |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Rolf Kötter Rolf Kötter Rolf Kötter Andrew T Reid Andrew T Reid Antje Krumnack Egon Wanke Olaf Sporns |
spellingShingle |
Rolf Kötter Rolf Kötter Rolf Kötter Andrew T Reid Andrew T Reid Antje Krumnack Egon Wanke Olaf Sporns Shapley ratings in brain networks Frontiers in Neuroinformatics sulcal length connectivity Game theory graph analysis Neural Network |
author_facet |
Rolf Kötter Rolf Kötter Rolf Kötter Andrew T Reid Andrew T Reid Antje Krumnack Egon Wanke Olaf Sporns |
author_sort |
Rolf Kötter |
title |
Shapley ratings in brain networks |
title_short |
Shapley ratings in brain networks |
title_full |
Shapley ratings in brain networks |
title_fullStr |
Shapley ratings in brain networks |
title_full_unstemmed |
Shapley ratings in brain networks |
title_sort |
shapley ratings in brain networks |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Neuroinformatics |
issn |
1662-5196 |
publishDate |
2007-11-01 |
description |
Recent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the application of graph theoretical concepts to the analysis of these structures within their large-scale connectivity networks. In this paper, we explore the application of concepts from graph and game theory toward this end. Specifically, we utilize the Shapley value principle, which assigns a rank to players in a coalition based upon their individual contributions to the collective profit of that coalition, to assess the contributions of individual brain structures to the graph derived from the global connectivity network. We report Shapley values for variations of a prefrontal network, as well as for a visual cortical network, which had both been extensively investigated previously. This analysis highlights particular nodes as strong or weak contributors to global connectivity. To understand the nature of their contribution, we compare the Shapley values obtained from these networks and appropriate controls to other previously described nodal measures of structural connectivity. We find a strong correlation between Shapley values and both betweenness centrality and connection density. Moreover, a stepwise multiple linear regression analysis indicates that approximately 79% of the variance in Shapley values obtained from random networks can be explained by betweenness centrality alone. Finally, we investigate the effects of local lesions on the Shapley ratings, showing that the present networks have an immense structural resistance to degradation. We discuss our results highlighting the use of such measures for characterizing the organization and functional role of brain networks. |
topic |
sulcal length connectivity Game theory graph analysis Neural Network |
url |
http://journal.frontiersin.org/Journal/10.3389/neuro.11.002.2007/full |
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