Journal of Mathematical Chemistry

, Volume 47, Issue 4, pp 1209–1223

Centrality measure in graphs

Original Paper

DOI: 10.1007/s10910-009-9635-0

Cite this article as:
Klein, D.J. J Math Chem (2010) 47: 1209. doi:10.1007/s10910-009-9635-0


Centrality of an edge of a graph is proposed to be viewed as a degree of global sensitivity of a graph distance function (i.e., a graph metric) on the weight of the considered edge. For different choices of distance function, contact is made with several previous ideas of centrality, whence their different characteristics are clarified, and strengths or short-comings are indicated, via selected examples. The centrality based on “resistance distance” exhibits several nice features, and might be termed “amongness” centrality.


Centrality Betweenness Shortest-path centrality  Resistance-distance centrality Graph metrics Neighborliness centrality 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Texas A&M University at GalvestonGalvestonUSA