Optimizing Pinning-Synchronization and Mining Pinned-Nodes of Directed Networks

Pinning control provides an effective approach to controlling large-scale networks and conserving control resources. This article presents a solution to pinning synchronization in directed networks with a precise index that measures the pinning synchronization capability of directed networks, capturing full topological information about the networks. Building upon this index, the article utilizes matrix analysis tools, such as the non-negative matrix theory and strongly connected decomposition to analyze the impact of network structures and controller parameters on the network synchronizability. Specifically, the study investigates the influence of the in-degree of unpinned nodes, the difference between in-degrees and out-degrees of nodes, strong connectivity components, and the linear feedback control gains on the network synchronizability. Moreover, the article addresses the challenge of optimally selecting pinned nodes by using a graph partitioning algorithm and a greedy node selection algorithm, which can be applied to effectively select pinned nodes in a large-scale network. Extensive simulations on a range of real-world directed networks validate the efficiency of the proposed algorithms and demonstrate their superiority over seven baseline algorithms.