The Efficiency Of Random Walks Of Several Families Of Generalized Weighted Networks

With the rapid development of the Internet,how to improve the efficiency of information transmission has become a hot topic,an effective measurement of the efficiency of information transmission is the random walks time.It is a major challenge to explore the relationship between random walks time and network topology,and control the efficiency of random walks.At present,the research focuses on unbiased random walks,but does not pay attention to the weighted network and the efficiency of biased random walks.Based on this issue,we study the random walks of several families of generalized weighted recursive networks and explore the effect of edge weight and biased parameters on the efficiency of random walks.The detailed studies are as follows:Chapter 1 introduces the knowledge about complex networks,the background and current situation of fractal networks and scale-free networks,and explains the significance of unbiased and biased random walks.Chapter 2 proposes a family of generalized and weighted transfractal networks,and obtains the analytical expression of the first return time(FRT)for a prescribed initial hub node by employing the self-similarity and the probability generating function,and obtains the scalings of the mean and variance of FRT with regard to network size.For a large network,the efficiency of random walks relates strongly with the weight factor.The smaller the weight,the better the efficiency bears.Finally we show that the variance of FRT decreases with more number of initial nodes,implying that our method is more effective for large-scale networks and the estimation of the mean FRT is more reliable.In Chapter 3,we propose a family of weighted scale-free networks with a trap in hub node and explore the effect of edge weight and the number of nodes in the initial state on the trapping efficiency.We obtain the exact solution of the average trapping time,shows that the smaller the number of nodes in the initial state and the edge weight,the smaller the average trapping time bears,the higher the trapping efficiency is,also the average trapping time grows as a power-law form with network size.In Chapter 4,we study the effect of biased delay probability and edge weight on trapping efficiency.By employing the network evolution law and self-similarity,we derive the average trapping time of biased random walks.The results show that the smaller theweight and the biased delay probability,the smaller the average trapping time bears and the higher the trapping efficiency is.Chapter 5 is a summary of this dissertation and the future work.