How Centrality of Driver Nodes Affects Controllability of Complex Networks.

Recently, the controllability of complex networks has become a hot topic in the field of network science, where the driver nodes play a key and central role. Therefore, studying their structural characteristics is of great significance to understand the underlying mechanism of network controllability. In this paper, we systematically investigate the nodal centrality of driver nodes in controlling complex networks, we find that the driver nodes tend to be low in-degree but high out-degree nodes, and most of driver nodes tend to have low betweenness centrality but relatively high closeness centrality. We also find that the tendencies of driver nodes towards eigenvector centrality and Katz centrality show very similar behaviors, both high eigenvector centrality and high Katz centrality are avoided by driver nodes. Finally, we find that the driver nodes towards PageRank centrality demonstrate a polarized distribution, i.e., the vast majority of driver nodes tend to be low PageRank nodes whereas only few driver nodes tend to be high PageRank nodes.