Unveiling Influence in Networks: A Novel Centrality Metric and Comparative Analysis through Graph-Based Models

Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and viruses. Several methods have emerged to pinpoint these influential entities in networks, represented as graphs. In these graphs, nodes correspond to individuals and edges indicate their connections. This study focuses on centrality measures, prized for their straightforwardness and effectiveness. We divide structural centrality into two categories: local, considering a node's immediate vicinity, and global, accounting for overarching path structures. Some techniques blend both centralities to highlight nodes influential at both micro and macro levels. Our paper presents a novel centrality measure, accentuating node degree and incorporating the network's broader features, especially paths of different lengths. Through Spearman and Pearson correlations tested on seven standard datasets, our method proves its merit against traditional centrality measures. Additionally, we employ the susceptible-infected-recovered (SIR) model, portraying virus spread, to further validate our approach. The ultimate influential node is gauged by its capacity to infect the most nodes during the SIR model's progression. Our results indicate a notable correlative efficacy across various real-world networks relative to other centrality metrics.