Closeness centrality in some splitting networks

Abstract

A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks, and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. \textit{Centrality} parameters play an important role in the field of network analysis. Numerous studies have proposed and analyzed several \textit{centrality} measures. We consider \textit{closeness centrality} which is defined as the total graph-theoretic distance to all other vertices in the graph. In this paper, closeness centrality of some splitting graphs is calculated, and exact values are obtained.

Keywords

• Graph theory
• network design and communication
• complex networks
• closeness centrality
• splitting graphs