ABSTRACT
The important nodes of a complex network is defined as some special nodes that can aect the structure and function of the network to a greater extent compared to other network notes, which is a network structure constructed with a huge number of nodes and the complex relationships between them . In mathematical description, it is a diagram with enough complex topology features [1]. Put it into the real world, when nodes are used to represent all sorts of individuals while edges represent the links between individuals, many things can be analyzed with the network graph theory. Numerous studies have shown that complex network possesses the small-world property [2], scale-free property [3], robustness against random attacks, vulnerable to malicious attacks and so on. To the study of complex network getting deep, discussions of many basic issues become more important. It is of high practical value to explore the important nodes in the network and assess their importance. This paper firstly introduces several research methods on the importance of the important node in complex network in recent years, and on the basis of the previous study, we proposed an evaluation method on the importance of important nodes in the weighted complex network based on PageRank. This method not only reveals the characteristics of the network topology structure, but also accurately reflect the relative importance of the nodes. Result of the experiment shows that this evaluation method based on PageRank performs eective with low overhead, and its operation speed is fast. It can get a perfect calculation capability in large-scale complex network
2 RELATED WORKS
There are lots of methods of evaluating the importance of nodes in complex networks, most of which are based on graph theory and data mining. Initial research originated in the field of sociology, then researchers from other scopes begun the study of such problems, too. To sum up, the main research methods are as follows:
1 Sorting method based on neighbor node. A class of the most simple and intuitive method, with degree centrality [4] investigating the number of direct neighbors of nodes, which believes that the larger number of neighbors a node owns, the bigger influence it will have; Chen et al. [5] considered the information of neighbor nodes in 4 layers with semi-local centrality; Kitsak et al [6] proposed to determine the location of nodes in the network using k-shell decomposition, which can be seen as an extension of degree centrality. It defines the importance of nodes according to their positions in the network with the view that the more a node is close to the core, the more importance it has.
