Study Of Nodes Influence In Complex Network Based On K-shell Decomposition

With the advent of technology, we have in-depth studies in complex network. As a new-rising subject, it has already come into our daily life now. From the specific aspect to the abstract aspect, such as traffic network, river network, social network, and internet network and so on, all of them are within the scope of the study. Complex network is an interdisciplinary subject. It contains physics, biology, sociology, management and so on. The research contents of complex network contains the structure of complex network, the character of complex network and the nodes influence of complex network and so on. By the way, the research of nodes influence in complex network is the main work of this paper. The study of nodes influence is significant to people’s life. The study of traffic network will help us to avoid traffic congestion and traffic accident et al. The study of social network will help human to isolate infection sources and break the chain of transmission.At present, the research of nodes influence has fruitful achievements, such as degree centrality, betweenness centrality, eigenvector centrality, k-shell decomposition and so on.Although there are so many method to evaluate nodes influence, these method still has its own defect. And researchers are always trying to look for a more effective, more precise and easier method to evaluate nodes influence in complex network. In this paper, firstly, we introduced the history of complex network and related statistical property of complex network.Secondly, we introduced some common methods of evaluating nodes influence in complex network. These common methods include degree centrality method, path-based method,feature vector method, random walker method and nodes location method. And then, we proposed two methods to evaluating nodes influence. One of these method is an improved k-shell decomposition based on potential weights. Another method is k-shell decomposition based on effective distance.The main work of this paper could be summarized as follows:a) Proposed an improved weighted k-shell decompositionThe existing weighted k-shell decomposition is defective in calculating weighted degree.So we improved the existing weighted k-shell decomposition via improving the method of calculating weighted degree in this paper. To verify the performance of improved method,we did some experiments in six real networks, Blogs, Email, Net-science, Roget, USAir and Yeast. In the SIR spreading experiment, the improved method could get more infected nodes after the model getting balance. The result of SIR spreading method shows that improved method is better than existing method for top-30 nodes. In the vulnerability experiment, the top-30 nodes of improved method could get bigger value than the top-30 nodes of existing method. The result of vulnerability experiment shows that the top-30 nodes of improved method is more influential than the top-30 nodes of existing method. And it further proves that the improved method is superior to existing method.b) Proposed a k-shell decomposition based on effective distanceCommon method based on k-shell decomposition consider factors often including weight and unweight et al. But never take the effective distance into consideration. Now, we proposed a k-shell decomposition based on effective distance in this paper. To verify the performance of our method, we did two experiments in four real networks, C.elegans, netscience, polblogs and USairport. The experiment results is showed as follows:In C.elegans network, the k-shell decomposition based on effective distance is better than the two other methods obviously. In the netscience network, the classical k-shell decomposition is better than k-shell decomposition based on effective distance. In the polblogs network, k-shell decomposition is better than the two other methods inconspicuously. In the USAirport network, the better than the two other methods obviously. To sum up, the k-shell decomposition method based on effective distance is superior to the exiting k-shell decomposition in most case.