Relative edge betweenness centrality

Damir Vukičević, Riste Škrekovski, Aleksandra Tepeh

Abstract


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.


Keywords


Centrality measures, betweenness centrality, social networks

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications