Eigenvector Centrality: Illustrations Supporting the Utility of Extracting More Than One Eigenvector to Obtain Additional Insights into Networks and Interdependent Structures
Journal of Social Structure, 18 (2), 1-22, 2017
22 Pages Posted: 11 Oct 2017 Last revised: 18 Nov 2017
Date Written: October 1, 2017
Among the many centrality indices used to detect structures of actors’ positions in networks is the use of the first eigenvector of an adjacency matrix that captures the connections among the actors. This research considers the seeming pervasive current practice of using only the first eigenvector. It is shows that, as in other statistical applications of eigenvectors, subsequent vectors can also contain illuminating information. Several small examples, and Freeman’s EIES network, are used to illustrate that while the first eigenvector is certainly informative, the second (and subsequent) eigenvector(s) can also be equally tractable and informative.
Keywords: centrality, eigenvector centrality, social networks
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