Node Ranking In Complex Networks

With the further study of complex networks, more and more scholars focus on the study of a small number of important nodes which have a huge effect on the function of entire network functions. Beaceuse the fast changing of size and structure of network, a more quickly and efficiently node ranking method becomes a research focus now and has important practical significance in all areas. This paper focuses on studies the node ranking in complex networks and the main contents are as follows:(1) This paper studies classical node ranking methods both in unweighted and weighted networks. The former contain degree centrality, closeness centrality, betweeness centrality, closeness centrality, Burt, PageRank, LeaderRank and the comparision of them; The latter contain weighted degree centrality, weighted closeness centrality, weighted PageRank, weighted LeaderRank and the comparision of them.(2) This paper puts forword the concept node similarity to measure the effect that a pair of nodes has on each other. On the basis of LeaderRank, this paper propose SRank which considers he difference influence. Unlike classical methods, SRank considers both local and global character of the topology so that the sort result is more accurate. What’s more, SRank can be applied to directed and undirected network.(3) The spreading importance of unweighted network is measured by SIR model. By the simulation on five real network and three evaluation methods: relevant picture, relevant index, the results show SRank is better than the other methods both in finding important nodes and nodes ranking. Besides, the computational complexity is very low which means SRank can be applied to large-scale network ranking.(4) On the basis of Burt, this paper consider the topology of nodes in two hops then puts forword W-Burt. W-Burt considers nodes centrality and bringe importance, making the results more accurate sorting. It’s corresponds to reality that despite of the small degree, the bringe node may have great power on promoting the speed of spreading.(5) The spreading importance of weighted network is measured by SI model. By the simulation on five real network and three evaluation methods: relevant picture, relevant index, the results show W-Burt is better than the other methods both in finding important nodes and nodes ranking. Besides, the computational complexity is very low which means it can be applied to large-scale network ranking.