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In the realm of network science, determining crucial nodes within a social network is an ongoing concern. As a result, it garners a lot of attention, and various centrality measures for the identification of crucial nodes have been proposed thus far. Degree and k-shell decomposition are the classic centrality measures that rely on neighboring nodes. However, degree, k-shell, and combination of degree and k-shell measures assign the identical value to the vast count of nodes, which creates a problem in distinguishing these nodes. Therefore, in this paper, for the purpose of solving the above problem, we propose an index based on three different components: degree, improved k-shell measure, and eigenvector centrality called the degree k-shell eigenvector (DKE) index. In addition, we propose an enhanced gravity model called the DKE-based gravity model (DKEGM) on the basis of universal gravity law and the proposed index for determining crucial nodes in social networks. The proposed gravity model incorporates different aspects of nodes, which include count of neighbors, location of nodes, influence of neighbors, and path information between the nodes. Numerous experiments are executed on eight real networks using the SIR model, Kendall tau, ranking monotonicity, and distinct metric to examine the effectiveness of the DKEGM with respect to the other measures. The empirical outcomes show the effectiveness of the DKEGM in terms of accuracy, distinguishing ability, and efficiency.

An Enhanced Gravity Model for Determining Crucial Nodes in Social Networks Based on Degree K-shell Eigenvector Index