Study On Average Trapping Time And The Average Shortest Path On Three Classes Of Weighted Networks

This paper mainly studies the average trapping time,the average shortest distance of the weighted pseudofractal scale-free networks under weight-dependent walk,and the stationary distribution,the average trapping time and the global mean first-passage time of the weighted rose networks under maximal entropy walk,the eigentime identity of the weighted(m,n)-flower networkIn Chapter 1,we introduces the origin and representation of complex and weighted networks,and briefly expounds the concept of some performance indicatorsIn Chapter 2,we study the average trapping time and the average shortest distance of the weighted pseudofractal scale-free networks with trap points.Under weight-dependent walk,we obtain the exact expression and the leading scaling of the average trapping time,and we find that the average trapping time of the weighted pseudofractal scale-free networks is the same as that of the unit weight pseudofractal scale-free networks.At the same time,in order to better understand the pseudofractal scale-free networks,we also studied the modified weighted pseudofractal scale-free networks,and obtained the leading scaling of the average shortest distance.We found that the average shortest distance would show different function curves in different weight factorsIn Chapter 3,we study some performance indexes of the weighted rose networks under two kinds of biased walks(weight-dependent walk and maximum entropy walk)the stationary distribution,the average trapping time and the global mean first-passage time.We obtain exact expressions of the stationary distribution and the average weighted trapping time under two kinds of biased walks,and we find that under the maximum entropy walk,there is a stable relationship between the weight factor and the trap process.The effectiveness of the trap process is also obtained by numerical simulation under the weight-dependent walkIn Chapter 4,the eigentime identity of weighted(m,n)-flower networks is studied By using the Vieta's formulas and the Markov matrix,we obtain the specific expression of the eigentime identity without the specific Laplace spectrum of the network.Then we demonstrate the influence of weighting factors on the eigentime identity by numerical simulation.