Centrality-Based Sombor Index for Network Systems with Applications to Molecular Chemistry and Disease Transmission Networks

A number is a graphical invariant in graph theory if it is invariant under graph automorphism. In molecular graph theory, graphical invariants are known as topological indices. Centrality measures are crucial aspects of social network analysis. Centrality measures are used to find famous or influential nodes in a network. These metrics offer valuable insights into the dynamics and structure of numerous networks, including social, transportation, biological, and communication networks. This article discusses a new approach to the Sombor Topological Index based on centrality measures. Due to the high application of centrality measures and topological indices, research has been going on on this topic. In this article, we have introduced some general ideas about centrality measures and topological indices. Then, we introduced a new centrality metric, Neighborhood-Closeness Centrality, and compared it with some existing centrality measures. We also discussed some of its applications. Then, we modified the Sombor Index and developed the Neighborhood-Closeness Centrality-Based Sombor Index, discussed some theorems on the Neighborhood-Closeness Centrality-Based Sombor Index, and discussed its applications in molecular chemistry and disease transmission networks. Finally, we have concluded this article with some future works.