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Correlations among centrality indices and a class of uniquely ranked graphs
Institution:1. Department of Computer & Information Science, University of Konstanz, Germany;2. Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA;1. Florida State University, United States;2. University of Ljubljana, Slovenia;3. University of Pittsburgh, United States;1. ETH Zürich, Chair of Social Networks, Clausiusstrasse 50, 8092 Zürich, Switzerland;2. University of Oxford, Nuffield College, New Road, Oxford OX1 1NF, United Kingdom;3. University of Groningen, Department of Sociology, Grote Rozentstraat 31, Groningen 9712 TG, The Netherlands;4. MTA-TK “Lendület” Research Center for Educational and Network Studies, [Hungarian Academy of Sciences], Országház utca 30, Budapest 1014, Hungary;1. Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China;2. School of Computer Science, Southwest Petroleum University, Chengdu 610500, China;3. Section for Science of Complex System, Medical University of Vienna, Vienna 1090, Austria;4. Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China;5. Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
Abstract:Various centrality indices have been proposed to capture different aspects of structural importance but relations among them are largely unexplained. The most common strategy appears to be the pairwise comparison of centrality indices via correlation. While correlation between centralities is often read as an inherent property of the indices, we argue that it is confounded by network structure in a systematic way. In fact, correlations may be even more indicative of network structure than of relationships between indices. This has substantial implications for the interpretation of centrality effects as it implies that competing explanations embodied in different indices cannot be separated from each other if the network structure is close to a certain generalization of star graphs.
Keywords:Network centrality  Correlation  Neighborhood inclusion  Centrality indices  Threshold graphs
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