Statistical Analysis on the Topological Indices of Clustered Graphs

Abstract

AbstractClustering deals with different kinds of attributes to identify communities within large groups. Clustered graph is a graph which obtained algorithmically by taking the edge structure of the graph in such a way that there should be many edges within each cluster and relatively few between the clusters. It is widely used in many fields such as data mining, pattern recognition, IMRT segmentation, telecommunication, radar detection, image processing, networking, etc. Nowadays, researchers scrutinize the concepts of topological indices such as, Randic index, Zagreb index, and atom-bond connectivity index which are exploited to estimate the bio-activity of chemical compounds and the premises of topology in networking. In this paper, clustered graphs have been originated from an algorithm. Degree-based indices such as Randic, first and second Zagreb, first and second multiplicative Zagreb, hyper Zagreb, atom-bond connectivity (ABC), inverse sum indeg, and geometric indices of the clustered graphs have been computed. Moreover, the regression analysis on Randic, SCI, ABC, ISI, and GA indices of the clustered graphs have been established which intreprets that those indices are highly correlated with \(R=0.99\). ...KeywordsZagreb indicesAtom-bond connectivity indexGeometric arithmetic indexInverse sum indeg indexClustered graphInterconnection networks.