On the centrality of some graphs

Yıl 2017, Cilt: 5 Sayı: 4, 1 - 11, 01.10.2017

Vecdi Aytac

Öz

  A central issue in the analysis of complex networks is
the assessment of their stability and vulnerability. A variety of measures have
been proposed in the literature to quantify the stability of networks and a
number of graph-theoretic parameters have been used to derive formulas for
calculating network reliability. Different measures for graph vulnerability
have been introduced so far to study different aspects of the graph behavior
after removal of vertices or links such as connectivity, toughness, scattering
number, binding number, residual closeness and integrity. In this paper, we
consider betweenness centrality of a graph. Betweenness centrality of a vertex
of a graph is portion of the shortest paths all pairs of vertices passing
through a given vertex. In this paper, we obtain exact values for betweenness
centrality for some wheel related graphs namely gear, helm, sunflower and
friendship graphs.

Anahtar Kelimeler

Network vulnerability, Network design and communication, Stability, Betweenness centrality of a graph, Gear graph, Helm graph

Kaynakça

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