Pinning a complex network through the betweenness centrality strategy

In this paper, we propose a new selective pinning strategy, the BC-based pinning strategy, to control a complex network, i.e., placing the local feedback controllers on the vertices with high betweenness centrality (BC). To verify that the stabilizability bounds of a network depend on not only degrees of the pinned vertices, but also the distance between the pinned vertex set and the unpinned vertex set, we pin two real-world networks, the protein-protein network in yeast and the U.S.A. airline routing map, through the BC-based strategy, where the vertices' BC are weakly correlated with their degrees. Since the vertex's BC contain more information with the degree as well as the shortest path, our investigation shows that the former method yields better stabilizability than the latter one.