The Research On Nodes' Control Capacities In Complex Networks

The final target of researching on complex networks is to control complex networks. Recently, the controllability of complex networks has been an essential direction in the field of complex networks. Following the development of it, study of complex networks' controllability is not only limited in the set of minimum driver nodes via networks' topology, but also covers many others, such as the relationships among controllability of complex and otherproperties, the ways to effectively control target nodes and the measurements of node importance in controllability of complex networks. The latter one is significant to understand and control complex networks.In 2013, an index to measure nodes' importance in controllability of complex network, called control capacity, was proposed.It describes the frequency of a node belonging to minimum driver nodes sets. And a random sampling algorithm was also given to effectively estimate nodes' control capacity without enumerating all maximum matched sets. This algorithm does greatly improve the efficiency of getting nodes' control capacities, but some shortages also exist. Therefore, this paper is to improve it.First, this paper studies the algorithm, does experiments on it, and gives a random sampling developing algorithm(RSDA), which can not only guarantee control capacity be effective, but can also solve the problem that old algorithm is invalid sometimes. Second, combining with the knowledge of probability distribution, this paper introduces different random function to influence the random sampling procedure. Specifically, this paper compare and analyze the efficiency and effect of RSDA with different random functions that respectively obey uniform distribution, exponential distribution, Gaussian distribution, binomial distribution and passion distribution. It is found that different random functions and different type of networks will have different influence on them. Moreover, the efficiency of RSDA will be obviously changed following the coefficient of different distribution. Finally, based on experiments and analysis, this paper respectively gives random sampling developing algorithm with suitable random functions to different types of networks. The better coefficients for them are also given. Especially, the exponentially distributed random functions with coefficient larger than 0.65 will have a good work in efficiency when nodes' control capacity are estimated in scale-free networks, whose topologies are similar to real networks. Such efficiency will be even higher 1 to 2 times than that applying in origin random function in the random sampling algorithm.