Study On Average Trapping Time And Coherence On Four Classes Of Weighted Networks

In this dissertation,we mainly study the average trapping time on the weighted scale-free treelike networks with biased walks,average trapping time on the weighted scale-free triangulation networks with biased walks,first-order network coherence of weighted fractal networks,and first-and second-order network coherence of weighted recursive trees.In Chapter 1,we introduce the background and development processes of complex networks and weighted networks,also introduce some performance indicators of weighted networks.In Chapter 2,we study two kinds of biased walks including standard weight-dependent walk and mixed weight-dependent walk on the weighted scale-free treelike networks with a trap.For the weighted scale-free treelike network,by the two methods of definition of the average trapping time(ATT)and eigenvalues of the fundamental matrix,we derive exact solutions and the leading scaling of the ATT measuring the efficiency of the trapping process.The obtained results show that the smaller value of the weight factor,the more efficient the trapping process is.In Chapter 3,based on the Chapter 2,we optimize the model and change the initial state of the network.The the initial state is a triangular connected graph,and the number of internal nodes is controlled by parameter.We obtain the weighted scale-free triangulation networks and related topological properties.For weighted scale-free triangulation networks,we study average trapping time with two kinds of biased walks,then analyze the influence of network parameters and weight factor on ATT,and verify the correctness of the leading scales of average trapping time with two kinds of biased walks by numerical simulation.In Chapter 4,we study the consensus dynamics with stochastic disturbances on a family of the weighted fractal networks.Network coherence is the robustness of consensus algorithms when the nodes are subject to external perturbations is studied.For the weighted fractal networks,by the relationship between the first-order network coherence and the entire mean first-passage time(EMFPT)for weight dependent walk which are all related to the Laplacian eigenvalues,the asymptotic behavior of the first-order network coherence is obtained through the exact expression of EMFPT.The obtained results show that the scalings of first-order coherence with network size obey three laws according to the range of the weight factor.In Chapter 5,for the family of the weighted recursive trees,through the uniformity and hierarchy of the network structure,we study the first-and second-order network coherence quantifying as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues on a family of the weighted recursive trees is constructed.Different from Chapter 4,we mainly obtainthe exact expressions and scalings of network coherence on the family of weighted recursive trees by the Laplacian eigenvalues,so as to avoid the tedious process of calculating.The obtained results indicate that the efficiency of network coherence on the weighted network has close relation to the weight distribution.