Analysis of Kapferer Mine Network using Graph Energy Ranking

Abstract

Vertex centrality is one of the procedures to evaluate complex networks, and it can disclose current patterns of networks. By evaluating their structural characteristics, it enables us to understand networks and their elements. One of the complex networks of nodes and interactions is the social network. It is increasing very greatly every day owing to the addition of fresh nodes. In such a vast network, therefore, not all nodes are equally essential, identifying influential nodes becomes a practical issue. To quantify the significance of nodes in networks, centrality measures were implemented. The multiple criteria are used to select critical nodes in the network. Various centrality measures such as Betweenness Centrality, Degree Centrality, Closeness Centrality, and some well-known centrality measures are therefore used to define vital nodes. In this article, we suggested a centrality to rank the nodes using a graph invariant called graph energy named as Graph-Energy-Ranking (GER). GER provides a better knowledge of the current network by evaluating the effect of node deletion on graph connectivity and thus enables us to better understand and maintain the network. In the current paper GER is applied on well-known social network called Kapferer mine network and results have been discussed.