The interaction of size and density with graph-level indices |
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| Affiliation: | 1. Department of Robotics, Carnegie Mellon University, Pittsburgh, PA, USA;2. Department of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA, USA;3. Center for the Computational Analysis of Social and Organizational Systems, Carnegie Mellon University, Pittsburgh, PA, USA;4. H.J. Heinz III School of Public Policy and Management, Carnegie Mellon University, Pittsburgh, PA, USA;1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, USA;2. Department of Mathematics, University of Ioannina, Ioannina 45110, Greece;3. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, Bucharest, RO-010014, Romania;4. Simion Stoilow Institute of Mathematics of Romanian Academy, Research group of the project PN-II-RU-TE-2012-3-0161, P.O. Box 1–764, Bucharest 014700, Romania;1. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia;2. Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751, Australia;3. School of Physical Sciences, University of Tasmania, Private Bag 37, Hobart 7001, Australia;4. Mathematical Institute, School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, UK;5. School of Mathematics and Statistics, Newcastle University, Newcastle NE1 7RU, UK;1. University of Hawai‘i at Mānoa, United States of America;2. Santa Clara University, United States of America;3. Texas A&M University, United States of America |
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| Abstract: | The size and density of graphs interact powerfully and subtly with other graph-level indices (GLIs), thereby complicating their interpretation. Here we examine these interactions by plotting changes in the distributions of several popular graph measures across graphs of varying sizes and densities. We provide a generalized framework for hypothesis testing as a means of controlling for size and density effects, and apply this method to several well-known sets of social network data; implications of our findings for methodology and substantive theory are discussed. |
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