<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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...

Eigenvector Centrality: Illustrations Supporting the Utility of Extracting More Than One Eigenvector to Obtain Additional Insights into Networks and Interdependent Structures

Published Online: Mar 11, 2018

Page range: 1 - 23

DOI: https://doi.org/10.21307/joss-2018-003

Keywords
centrality, eigenvector centrality, social networks

© 2018 Dawn Iacobucci et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Eigenvector Centrality: Illustrations Supporting the Utility of Extracting More Than One Eigenvector to Obtain Additional Insights into Networks and Interdependent Structures

Published Online: Mar 11, 2018

Page range: 1 - 23

DOI: https://doi.org/10.21307/joss-2018-003

Keywordscentrality, eigenvector centrality, social networks

© 2018 Dawn Iacobucci et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
centrality, eigenvector centrality, social networks