Application Of Centrality Index For Control And Prediction Of Networks

In many real networks, we feel intuitively that some vertices and edges are more central than others, and we may usually need to compare their centrality. Evaluation and comparison of vertex and edge centrality is not only helpful to describe the characteristics of networks, but also crucial for controlling and predicting network dynamics. Centrality indices provide us a tool to quantify centrality of vertices and edges, by which we can explore efficiently the implicative information of vertices and edges.In the research of complex networks, centrality index has been investigated for a long time. Early centrality indices such as degree and betweenness have been widely used to characterize the network topology. Later on, different centrality indices have been proposed for various research needs of real networks. Some well known indices that has been applied to real networks include Impact Factor for scientific journal and PageRank used in search engine for ranking web pages'centrality in the World Wide Web.In this thesis, we review state-of-the-art of centrality index research, and propose a novel vertex centrality index, ControlRank, for pinning control of directed dynamical networks. We also analyze the application of a class of edge centrality indices, and investigate a method based on vertex similarity for link prediction of a commercial online network.The contributions of this thesis are as follows:1. By applying local feedback injections to a small fraction of network vertices, a dynamical network can be stabilized on a homogeneous equilibrium. However, different pinning strategies may result in different performances. We develop a novel pinning scheme based on ControlRank. ControlRank makes full use of the link structure of the directed networks, and the factors affecting ContralRank are related to the lower bound of pinning stabilizability in dynamical networks.Simulation studies performed on scale-free directed dynamical networks and Ring-Star models demonstrate that it is much more effective to pin the vertex with largest ControlRank than pin the vertex with largest out-degree.2. The link-prediction problem infers the new possible edges in future by a snapshot of the network. The location of new edges is determined by the edge centrality of unlinked pairs of vertices, which is quantified by different link-prediction approaches. In the special case of a commercial online network, Wealink, structure similarity of vertex measures the similarity relationship of commercial status between individuals in the social network. By comparing the performances of various link-prediction methods applied to Wealink, we verify that the method based on vertex similarity is a reasonable simulation for the people's behavior of extending on-line commercial relationships.