Robustness Analysis Of Complex Network Control And The Research Of Optimal Selecting Algorithm Of Driver Node Set

In the real world, many systems exist in the form of directed complex networks. In order to make these systems run formally, we must control the whole system. Mapping the complex networks on linear system, we apply the maximum matching algorithm of bipartite graph and treat unmatched nodes as driver nodes to get a minimum driver node set. We can realize the effective control of the complex network by inputting the driver nodes into external signals. Controlling robustness of complex network means that when a node of network can’t receive external control signals due to outside influence or own cause, we can use other nodes to replace the failed nodes to effectively control the network by receiving an external signal. These nodes can make network reach expected status finally.According to what possibility of replacing failed node; how to find the replacing node; how to calculate the robust number of drive nodes set, we research the controlling robustness of complex network. Major findings of the current study are recapped as follows:(1) First, this thesis proposes three theorems of controlling robustness. These theorems are reversal matching theorem, judgment theorem and robustness of driver node set of theorem. Then, according to three theorems, this thesis proposes two algorithms to judge K failed driver nodes and to calculate the robust number of drive node set. Finally, we conduct experiments in real world, BA scale-free networks and ER random networks to test their effectiveness. The results show that the robust number of driver node set is closely related to network topology. The average degree ofthe network has great influence on the robust number of drive node set.(2) Due to many driver node sets existing in the network and the different controlling cost of these driver node sets, we regard the robust number of driver node set as a standard which can measure controlling cost of network. There are more robust numbers, the robustness of network is better. This thesis proposes an optimal selecting algorithm of driver node set According to this algorithm, we can get a best driver node set that having max robust number.