Controllability and observability analysis for vertex domination centrality in directed networks

Topological centrality is a significant measure for characterising the relative importance of a node in a complex network. For directed networks that model dynamic processes, however, it is of more practical importance to quantify a vertex's ability to dominate (control or observe) the state of other vertices. In this paper, based on the determination of controllable and observable subspaces under the global minimum-cost condition, we introduce a novel direction-specific index, domination centrality, to assess the intervention capabilities of vertices in a directed network. Statistical studies demonstrate that the domination centrality is, to a great extent, encoded by the underlying network's degree distribution and that most network positions through which one can intervene in a system are vertices with high domination centrality rather than network hubs. To analyse the interaction and functional dependence between vertices when they are used to dominate a network, we define the domination similarity and detect significant functional modules in glossary and metabolic networks through clustering analysis. The experimental results provide strong evidence that our indices are effective and practical in accurately depicting the structure of directed networks.