Centrality in partitioned networks

Francesco Ciardiello and Andrea Di Liddo

Abstract

We present a mathematical model based on partitioned networks. Networks with a coalition structure are embedded in social networks, financial networks, segmented markets, the theory of weak and strong ties, intermodal logistics and statistical detection of communities. We define new centrality measures through the means of cooperative game theory. A centrality measure ranks nodes because of their relevance or importance against a specific phenomenon or in absolute sense. Just to simplify, the most influential spreader of COVID-19 virus has the highest centrality across two coalitions: vaccinated and unvaccinated individuals.