Research On Influential Nodes Based On Vital Communities

As a booming research field in data mining,complex network analysis is attracting more and more researchers' attention.To dig the different structural and functional characteristics of the network,the research focus on the fields ranged from community structure on the mesoscopic perspective to influential nodes on microscopic perspective.On the one hand,community detection is a very essential basic work in the research of complex networks.It provides a method for more accurate research and understanding of the network topology,physical meaning and functional behavior from the perspective of divide and conquers.On the other hand,given the significant differences in function and structure among nodes in the network,how to identify specific nodes in functions and institutions also has significance of importance.At present,scholars around the world have done a lot of research work on ranking the importance of nodes,ranging from the intuitive and easy-to-understand perspective,such as the number of nodes' neighbors and relatively path,to the mathematical perspective like using eigenvectors on matrix.However,most of the work has not been combined with the meso-structure of complex networks due to the progress in related fields.For the research on the combination of vital nodes and the community structure in recent years,it is only considering the most basic concepts of the community without digging and exploiting it deeply.At the same time,the direction of the edges is also a factor on effecting the importance of nodes on the directed networks,which is not considered on the related study.Based on the existing researches,we discuss the importance of nodes based on the community detection and complete the following major work.First,based on the proposed ClusterRank algorithm,the improved node importance index IO-ClusterRank is given by combining with the contribution of the edge direction in weighted directed network.The ranking algorithm considers the influence of the out-degree neighbors and in-degree neighbors of the nodes on their importance and distinguishes them respectively.At the same time,the sorting algorithm also takes the contribution of edge weights to the importance of the nodes as a reference factor.Second,on the basis of a comprehensive comparative analysis of the current major structural hole definitions,we propose the concept of important communities by combining the related community detection algorithm and the importance index of nodes.Then referring to the main idea of structure hole theory and ranking the importance of nodes,we propose a node importance ranking algorithm based on important communities,which repute that it is more important for nodes in important communities who connect more nodes in important communities.The algorithm evaluates importance of nodes based on the situation of nodes connected to their own communities and the situation of connecting other communities outside their own communities.Third,based on the actual data set,the IO-ClusterRank index mentioned above and the node importance evaluation index based on the important community were tested and analyzed.On the one hand,in three weighted directed networks with different scales and in-out degree distributions,the SIR model and Kendall's tau correlation coefficient are used to evaluate and analysis differences on IO-clusterRank indicator and other important indices on weighted directed networks.The results indicate that the improved indicator has advantage on directed networks with unbalanced in-out degree.On the other hand,in four social networks of different sizes,we compare and analysis differences between the importance index of nodes based on the important communities and other major traditional node importance indices on the propagation capability of the SIR model and the robustness of the deleted node using the igraph package in Python.The results show that the index we proposed has advantage on networks with clear community sttucture.