Relative edge betweenness centrality

Authors

  • Damir Vukičević
  • Riste Škrekovski
  • Aleksandra Tepeh

DOI:

https://doi.org/10.26493/1855-3974.863.169

Keywords:

Centrality measures, betweenness centrality, social networks

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.

Published

2016-12-09

Issue

Section

Articles