Geodesic
Relative edge betweenness centrality
Ars Mathematica Contemporanea, Tome 12 (2017) no. 2, pp. 261-270.

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We introduce a new edge centrality measure - relative edge betweenness γ(uv) = b(uv) /√(c(u)c(v)), where b(uv) is the standard edge betweenness and c(u) is the adjusted vertex betweenness. In this alternative definition, the importance of an edge is normalized with respect to the importance of its end-vertices. This gives a better presentation of the “local” importance of an edge, i.e. its importance in the near neighborhood. We present sharp upper and lower bounds on this invariant together with the characterization of graphs attaining these bounds. In addition, we discuss the bounds for various interesting graph families, and state several open problems.
DOI : 10.26493/1855-3974.863.169
Keywords: Centrality measures, betweenness centrality, social networks 
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Damir Vukičević; Riste Škrekovski; Aleksandra Tepeh. Relative edge betweenness centrality. Ars Mathematica Contemporanea, Tome 12 (2017) no. 2, pp. 261-270. doi : 10.26493/1855-3974.863.169. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.863.169/

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