Distributed Estimation and Control of Node Centrality in Undirected Asymmetric Networks

Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this article, we address the problems of distributed estimation and control of node centrality in undirected graphs with asymmetric weight values. In particular, we focus our attention on alpha-centrality, which can be seen as a generalization of eigenvector centrality. In this setting, we first consider a distributed protocol where agents compute their alpha-centrality, focusing on the convergence properties of the method; then, we combine the estimation method with a distributed iteration to achieve a consensus value weighted by the influence of each node in the network. Finally, we formulate an alpha-centrality control problem, which is naturally decoupled, and thus, suitable for a distributed setting and we apply this formulation to protect the most valuable nodes in a network against a targeted attack, by making every node in the network equally important in terms of alpha-centrality. Simulations results are provided to corroborate the theoretical findings.