Closeness Centrality Weight of Graphs Under Some Graph Operations - Mathad, Veena; Pavithra, M. (Communications in Mathematics and Applications, 2025)
Many complex systems exhibit a natural hierarchy in which elements can be ordered according to a notion of influence with closeness centrality being one of the three well-known centrality measures used in social network analysis, determining the importance of vertices in a network, a core task in each network application. It describes the relative importance of a single vertex within a network or graph by finding the average proximity of that vertex to all others in that graph. In this paper, we derive formulae for the closeness centrality weight of the graph resulting from the operations between some graph families namely, join graph, Cartesian product of graph, shadow graph, corona graph, lexicographic product, disjunction graph and total graph.