Research On Nodes Importance In Complex Networks

In real life, the network exists everywhere, such as the traffic network, customer relationship networks, Internet networks, scientific collaboration networks, etc. In recent years, more and more researchers have focus on complex network. In particular, many of the real networks showed some characteristics different from the previous network theories, such as the small-world effect, scale-free characteristics and level characteristics. With the deeply understanding of the structural characteristics of the network, research about survivability and reliability of complex networks is thriving. Who is the most active and influential person in social life which nodes sustain the maximum flow in communications and transportation network? Who are the most dangerous people in transmission of disease such as HIV? Such problems relate to the question how to depict the node position in network, which means the node importance. The key point of the research is to protect those nodes caused the greatest loss on network, namely the most important node of network. Therefore, effectively identifying important nodes in complex networks has very practical value.This paper studies the node importance evaluation method of complex network, the main work is as follows:Firstly, the paper introduced some classification of present node importance evaluation methods of complex network, and analyzed the characteristics of some common node importance indicators.Secondly, by analyzing the advantages and disadvantages of the degree centrality and closeness centrality, this paper proposed a new node importance evaluation method. The new is based on degree centrality and closeness centrality, then incorporated the adjacency matrix to construct node importance evaluation matrix. Experimental results show that the new node importance evaluation method can overcome defect of the degree centrality and closeness centrality, and this method can more effectively and accurately find the node importance of complex network when compared with betweenness centrality, module density centrality etc.Thirdly, by analyzing the advantages and disadvantages of the currently common node importance evaluation methods, this paper chooses degree centrality, closeness centrality,betweenness centrality and eigenvectors centrality four indicators to evaluate the nodes importance of the complex network. A multi-level gray relational analysis model is established to identify the correlation between node and the optimal node, in order to sort node importance of complex network. This model not only considered effect of the local and global characteristics of the network on node importance, but also considered the impact of the quality and quantity ofneighbor node and the transmission capacity of the network. Compared with the real network and other nodes importance methods, the method can accurately find important nodes of complex networks, and can effectively distinguish the importance of the node.