Research On The Maximum Structure Control For Directed Networks

Complex networks have constantly been in the focus of research for these years. The analysis and comprehension of complex networks can help us to understand the underlying structure and properties in the existing natural and biological systems, uncover the interaction between the nodes of networks, and to take full control of complex networks. Due to the intricate interaction of the nodes in the network, when some of the nodes received the control signals or structure perturbations may cause a massive effect in the structure of the network or the pathways of the message passing. As a consequence, in the research of complex networks, it is very important to choose the appropriate nodes to control the networks under our ambition when we put the control signals into these nodes.The main content of this paper will be shown in two parts:(1)We will combine the control theory and graph theory, using the maximum matching algorithm to find the minimum driver set in the network, making sure the whole system is controllable. Then apply to a simple model and real networks to analyse the properties of the networks through the analysis of the driver nodes and get the significance of the driver nodes in complex networks.(2)As there are amounts of nodes in the network, every node has its own role in controlling the network. It is efficient to analyse the robustness of complex networks to analyse the control centrality of nodes. Here we introduce the control centrality of a node, and use linear programming as an efficient numerical tool to calculate the control centrality and the structurally controllable subsystem of any node in an arbitrary complex networks via calculating the number of the edges of a particular subgraph in the graph(A, B). As the number of nodes in real networks is enormous, it is impossible for us to provide such a huge number of control signals in practical. To solve this problem, we present an algorithm called the optimum group centrality, which presents how to choose the appropriate nodes combinations to achieve the maximum control of the system when the number of control signals are fixed. Compare the algorithm with the ordinary one and find that our algorithm has better accuracy and is more efficient in controlling the networks.