Research On The Biased Random Walk And Coherence Of Self-similar Complex Networks

Complex systems exist widely in the fields of nature,human society,and financial systems.However,due to the large scale of the system and the complex relationships between system elements,it is difficult for people to understand the impact and role of its structure and micro-mechanisms on the entire system.The complex network is the epitome of the complex system.It regards the individuals in the system as nodes and the relationships between individuals as edges.By establishing a network model and analyzing the properties of the model,it provides powerful research tools and fresh research perspectives for people to understand complex systems and their dynamic behaviors.For example,researchers regards financial institutions in the financial system as nodes,and the connections between financial institutions as links,to study the transmission mechanism of systemic financial risks from the perspective of complex networks.In order to analyze and reveal the factors that affect the dynamic process of information dissemination in complex networks,surrounding the structure and dynamic indicators of typical complex networks,this paper selects two types of complex network models with self-similar structures,and uses statistical methods to study their dynamic properties.The main research contents of this paper are as follows:1.Research on biased walking of scale-free pseudo-fractal networks with trap nodes.As a form of the biased random walk,the lazy random walk is to add a self-loop jump with a certain probability at each network node,to transforms the standard random walk process,and it has been applied in scientific fields such as image segmentation and optimal transportation,but there are few theoretical studies on this dynamic process.This paper innovatively studies the lazy random walk problem with absorbing nodes on a scale-free pseudofractal network,and calculate the exact solution of the average trapping time(ATT)by two methods: renormalization group and probability generating function,the results that is obtained by the two methods are consistent.Comparing these results with the ATT under standard random walk,it can be found that adding self-loop jump to change the walk rule can affect the coefficient term of the ATT,but does not change the exponential term.2.Research on biased wandering of Koch network with trap nodes.In order to further analyze the influence of walk rules on network trapping efficiency,this paper studies the lazy random walk problem of Koch network with structure parameter 8),where parameter8)can adjust the structure of Koch network to make it show different network structure characteristics.Using the method of renormalization group,we obtained the analytical solution of the average trapping time of Koch network under lazy random walk,and verified the correctness of the analytical solution of ATT.Comparing the results of the two types of walks,and analysing the influence of network structure and walk rules on the network information dissemination efficiency,the results show that both adjusting the walk rule and changing the network structure in the Koch network can affect the coefficient term of the average trap time.That is to say,adjusting the walk rule for the trapping efficiency of the Koch network has a similar effect as changing the network structure.3.Research on the robustness of extended Koch network consensus.Under the control of different network parameters,the degree correlation of the extended Koch network can be assortative,disassortative or uncorrelation.we conclude the relationship between network coherence and network resistance distance,and given the upper and lower bounds of network consensus when the network scale is determined.Based on the self-similar structure of the extended Koch network,we calculated the network resistance distance,and it is concluded that the two consensus indicators of the extended Koch network grow logarithmically with the network size,which suggests that the robustness of the extended Koch network consensus is independent of its degree correlation.In addition,the larger the adjustment parameter of the extended Koch network,the stronger the robustness of its network consensus.