Theoretical insights into closeness centrality enhance analysis of transportation networks and small-world networks, suggesting improved identification of influential nodes.
Centrality measurement is a useful way to find the most important points (vertices) and connections (edges) in a network. Over time, many researchers have created different types of centrality measures to study and understand how networks work. Closeness centrality, in particular, is crucial for examining biological, social, and transportation networks. The closeness centrality of a node u of a graph is the multiplicative inverse of the sum of the distances from u to each other vertex. We define normalized closeness centrality CNC(u) of a vertex u as CNC(u) = n-1∑x∈ Vd(u,x), where $n=|V|$. This centrality measurement is more receivable than degree centrality because it counts direct as well as indirect connections. In this paper, we present some new theoretical results for finding normalized closeness centrality of some corona product graphs like Pₙ Pₘ, Pₙ Kₘ, Cₙ Kₘ, Pₙ Cₘ, Cₙ Cₘ, Cₙ Pₘ, Pₙ Sₘ, Sₙ Kₘ, Kₙ Pₘ and Kₙ Kₘ. We also correct the result established by Eballe et al. for finding the vertex closeness centrality of the cycle graph Cₙ. The corona graph has many applications, including in signed networks, biotechnology, chemistry, and small-world networks. We demonstrate a practical application of our proposed results for identifying influential nodes in small-world networks based on our results and using the corona product graph model. We also present the applications of our studied results in a transportation network by transferring our crisp result to fuzzy membership degree and using the corona product graph model.
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Nandi et al. (2025) studied this question.
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