Graph Energy Based Centrality Measure to Identify Influential Nodes in Social Networks

One of the measures to analyze complex network is vertex centrality; it can reveal existing network patterns. It helps us in understanding networks. One of the measures to analyze complex network is vertex centrality, and it can reveal existing network patterns. It helps us in understanding networks and their components by analyzing their structural properties. The social network is one of the complex networks which is composed of nodes and relationships. It is growing very vastly due to the addition of new nodes every day. All nodes are not equally important in such a vast network hence, identifying influential nodes becomes a practical problem. Centrality measures were introduced to quantify the importance of nodes in networks. The various criterion is used to select critical nodes in the network. Therefore, different centrality measures like Betweenness Centrality, Degree Centrality, Closeness Centrality, and other well-known centrality measures are used to identify essential nodes. We have proposed an algorithm to compute a centrality using graph energy called Energy-Based-Centrality-Measure (EBCM) in this paper. It identifies the central nodes based on a graph invariant called graph energy. EBCM gives a better understanding of the current network by analyzing the impact of node deletion on graph connectivity and thereby helps us in achieving a better network understanding ability and maintenance.