
Contents
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The Walk Structure Perspective The Walk Structure Perspective
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The Contribution/Induced Centrality Perspective The Contribution/Induced Centrality Perspective
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The Flow Outcomes Perspective The Flow Outcomes Perspective
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Discussion Discussion
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Final Note Final Note
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Acknowledgments Acknowledgments
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References References
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17 Three Perspectives on Centrality
Get accessStephen P. Borgatti is the Paul Chellgren Chair of Management at the University of Kentucky, where he is also department head. He received his PhD in Social Science from the University of California, Irvine, and his BA in Anthropology at Cornell. His research interests are in social networks, particularly in flow phenomena and cognition about networks. He is a past president of International Network for Social Network Analysis (INSNA) and winner of the INSNA’s Simmel Award for lifetime achievement. He is coauthor of the UCINET software for social network analysis.
Martin G. Everett is currently codirector of the Mitchell Centre for Social Network Analysis at the University of Manchester and has over 40 years’ experience in research in social network analysis. He graduated in mathematics from Loughborough University and then went on to Oxford to complete a master’s degree and a doctorate. He is a past president of the International Network for Social Network Analysis, winner of the Simmel Award for lifetime achievement in social network analysis, coeditor of the journal Social Networks, coauthor of the social network analysis package UCINET, and a Fellow of the Academy of Social Sciences.
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Published:15 December 2020
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Abstract
This chapter presents three different perspectives on centrality. In part, the motivation is definitional: what counts as a centrality measure and what doesn’t? But the primary purpose is to lay out ways that centrality measures are similar and dissimilar and point to appropriate ways of interpreting different measures. The first perspective the chapter considers is the “walk structure participation” perspective. In this perspective, centrality measures indicate the extent and manner in which a node participates in the walk structure of a graph. A typology is presented that distinguishes measures based on dimensions such as (1) what kinds of walks are considered (e.g., geodesics, paths, trails, or unrestricted walks) and (2) whether the number of walks is counted or the length of walks is assessed, or both. The second perspective the chapter presents is the “induced centrality” perspective, which views a node’s centrality as its contribution to a specific graph invariant—typically some measure of the cohesiveness of the network. Induced centralities are computed by calculating the graph invariant, removing the node in question, and recalculating the graph invariant. The difference is the node’s centrality. The third perspective is the “flow outcomes” perspective. Here the chapter views centralities as estimators of node outcomes in some kind of propagation process. Generic node outcomes include how often a bit of something propagating passes through a node and the time until first arrival of something flowing. The latter perspective leads us to consider the merits of developing custom measures for different research settings versus using off-the-shelf measures that were not necessarily designed for the current purpose.
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