A Study on Measures of Central Tendency of Some Distance Parameters of Connected Graphs
This dissertation sets out to examine the implications of various mea- sures of central tendencies of graphs by introducing the unique concept of ?graphs. A ?graph is defined as a simple, finite, connected and undirected graph in which the basic centrality measures: mean, median and mode of eccentricities are equal. It takes a formal approach to the exploration of ?graphs by applying the principles of Graph Theory. Various graphs are looked into to compare the centrality measures, and the possibility of those being ?graphs. Earlier graph theoretical research in notions of centrality, distance and eccentricity are reviewed. It describes the development of a new elicitation tool that examines the effect of measures of central tenden- cies in graphs, by analyzing their eccentricity sequences. Using this new ap- proach the central values of certain graphs are obtained. The concept found would be helpful to develop a more complex interpretation of the notion of centrality measures in graph theory. Keywords: Eccentricity; Eccentricity sequence; Distance; Degree; Cen- trality; Mean; Mode; Median; ?graph; Central value