Minimum Distance Dominating Set in Complex Networks

Controllability of complex networks has recently become an important and fascinating issue in network science. One of the main frameworks proposed to control complex networks is minimum dominating set(MDS), which dominates complex networks by identifying driver nodes. For the MDS model, we mention that the driver node can only control its neighbor nodes, which means the value of the control distance is 1. However, in some real systems, important nodes cann't only control their neighbor nodes but also the nodes which are two hops away from them, which motivates us to explore the relationship between controllability of complex networks and control distance. In this paper, we first integrate key concepts from the theory of distance domination in graphs and apply them to the analysis of the controllability of complex networks. Further, we propose two methods to solve the model. Finally, we research on different kinds of complex networks parameters and their correlations with the percentage of driver nodes. Empirical analysis on artificial and real-world networks indicates that the networks are easier to control as the control distance or average degree increases.