Centrality-driven Sparse Optimal Control of Belief Formation in Social Networks

Abstract

 This paper studies the problem of steering collective beliefs in social networks when only a small fraction of nodes can be directly influenced. We propose a sparse optimal control framework built on the Network Drift-Diffusion Model (NDDM). Two intervention mechanisms are considered: direct control and latent (indirect) control. To select which nodes to actuate, we compare six centrality measures---Degree, Betweenness, Eigenvector, Closeness, PageRank, and K-shell---and keep only the top 5\%--30\% as control inputs. The optimal feedback law follows from the Hamilton-Jacobi-Bellman (HJB) equation, which reduces to solving Riccati-type differential equations. We test our approach on Erdős-Rényi (ER), Barabási-Albert (BA), and Watts-Strogatz (WS) networks. The results show that the best centrality choice depends strongly on the network topology, and the system undergoes phase transitions as control parameters vary.