IJPAM: Volume 103, No. 1 (2015)
Department of Mathematics
Faculty of Science
35100, Bornova, Izmir, TURKEY
Abstract. Networks are known to be prone to node or link failures. A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far.
The distance d(i,j) between any two vertices i and j in a graph is the number of edges in a shortest path between i and j. If there is no path connecting i and j, then
. Latora and Marchiori introduced the measure of efficiency between vertices in a graph in 2001. The unweighted efficiency between two vertices i and j is defined to be
for all . The global efficiency of a graph
which is simply the average of the efficiencies over all pairs of distinct vertices. In this paper, we study the global efficiency of special graphs. The behavior of this distance-related parameter on special graphs is taken into account by graphical analysis.
Received: March 13, 2015
AMS Subject Classification: 05C40, 68M10, 68R10
Key Words and Phrases: graph vulnerability, network design and communication, efficiency, global efficiency
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DOI: 10.12732/ijpam.v103i1.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 61 - 70