Research On The Structure And Dynamics In Multilayer Networks

The development of network science provides a new perspective for the analy sis of the struc-ture and dynamics of a large number of networked systems,and effectively reveals various dynamic phenomena that take place on independent networked systems.In fact,there are always various in-fluences between different systems,while completely independent networked systems are rare in the real world.Therefore,research methods based on traditional single-layer networks are no longer suitable for these interconnected systems.Multilayer network is a theoretical model that describes multiple networked systems that interact with each other,which has many structural and dynamical properties that are different from single-layer network.In recent years,although researchers have carried out a lot of research works in the field of multilayer networks,most of the current research work is unable to achieve systematic analysis of the relationships between structure and dynamics in multilayer networks.The shortcomings are mainly reflected in the following aspects:(1)In the aspect of multilayer network reconstruction,existing works usually follow the link prediction methods in single-layer network,and do not re-gard a multilayer network as a whole,ignoring the coupling relationship between different layers;(2)In terms of structural analysis,existing works are usually aimed at a certain type of multilayer network,or focused on a certain application,where the impact of different layers are cpredeter-mined.Thus,a structural analysis framework for multilayer networks remains lacked;(3)In terms of dynamic analysis,existing works usually establish a complicated theoretical model for a dynamic process,while too many parameters make it extremely difficult to analyze the dynamic process on a multilayer network.In view of the deficiencies of the existing research works,this dissertation studies and analyzes the relationships between structure and dynamics in a variety of multilayer network scenarios based on the latest research results,and establishes corresponding mathematical methods.The study of structure and dynamics provides a systematic analysis tool for theory and practice.The main contributions of this article are as follows:1.A brief review on the background and applications of multilayer networks,and a summa-rization for the research progress on the hot issues of structural and dynamical analysis in multilayer networks are provided.2.The inference of the complete structure of the multilayer network is studied,and a research method for the reconstruction of the multilayer network is proposed.This method is based on the maximum likelihood estimation theory and uses the aggregated network and parial structural information of the multilayer network to fully reconstruct the multilayer network.Facing the problem that maximum likelihood estimation has no closed-form solution,the expectation maximization algorithm is used to calculate the numerical results.In order to evaluate the reconstruction performance of the method,the reconstruction results are an-alyzed from the perspectives of link reliability,degree distribution and dynamic process.After that,in order to further analyze the reconstructability of multilayer networks,based on the theory of information entropy,an index describing the discrimination of multilayer network structure is proposed,which combines partial observations and several multilayer network structure characteristics.Through theoretical analysis,the proposed index directly determines the accuracy of the reconstruction of a multilayer network,thereby quantifying the reconstructability of a multilayer network.When given an observation budget,based on the analysis of the reconstructability of a multilayer network,the budget allocation strategy is theoretically obtained to reach the optimal reconstruction for a multilayer network.Through simulation experiments on several real multilayer networks and a large number of artificially generated multilayer networks,the validity of the theoretical analysis is verified3.The measurement of the eigenvector centrality in multilayer networks is studied,and an framework for analyzing eigenvector centrality in general multilayer networks is proposed This framework extends the eigenvector centrality in single-layer networks based on matrix computations to the eigenvector centrality in multilayer networks based on tensor computa-tions.Specifically,by introducing interlayer influence coupled with the multilayer network structure,the interaction between different layers is well described,in order to be valid for different scenarios and different types of multilayer networks.Then,by calculating the ten-sor product of the multilayer network structure and the interlayer influence,the interactions between each pair of nodes in the multilayer network can be quantitatively obtained.Facing the problem that the traditional power iteration method cannot converge,by introducing an it-confirmed erative compression factor,a compressed power iteration method is proposed to calculate the numerical solution of the centrality in the multilayer network.After that,two typical mul-tilayer network scenarios(that is,nodes are homogeneous while edges are heterogeneous,nodes and edges are heterogeneous at the same time)are used to specifically explain how to define interlayer influence.The existence and uniqueness of the eigenvector centrality in the multilayer network are also theoretically proved.The results of simulated random walk pro-cesses on real multilayer networks such as the Internet,transportation networks,and social networks show that the framework can describe the importance of nodes more accurately than the centrality analysis method for traditional single-layer networks,helping us to understand the intrinsic relationship between structure and dynamics in multilayer network.4.The relationship betwe en the temporal network structure and the transmission process is an-alyzed.Taking the epidemic of COVID-19 as an example,the correlation between the level of population contacts and the development of the epidemic is analyzed.Based on the sparse population movement trajectories in the epidemic area,a temporal contact network of the population is constructed to quantify the daily contacts between the infected and the suscep-tible individuals.In order to monitor the contact level in real time,five time-series indicators based on structure of the temporal contact network are introduced to reflect the dynamic re-sponse capabilities of epidemic prevention policies such as "lock down".In order to further analyze the intrinsic relationship between the population level and the epidemic,a correla-tion analysis is carried out between the number of cases and the contacts,including sensitivity analysis of various parameters,delay correlation of time series,and accumulative correlation,etc.Results of correlation analysis show that there is a strong correlation be-tween the structure of the temporal contact network and the transmission process(Pearson correlation coefficient is above 0.73).In the meantime,several important epidemiological parameters such as the population contact period,infection period and incubation period are effectively monitored.In order to achieve the accurate monitor of high-risk individuals,an infection risk assessment model is proposed based on the structural characteristics of the temporal contact network.The model is based on the Bayesian posterior estimation the-ory,leveraging the difference of daily contact behavior between the infected population and the uninfected population to quantify the infection probability of each individual.Finally,through the analysis of the receiver operating characteristic curve,it is revealed that the risk assessment model based on structure of the temporal contact network structure can measure the individual's infection risk more accurately than that drawn from the characteristics of age and gender.5.The content of the full text is summarized,the contribution of each chapter is summarized,and the direction of further research on the structure and dynamics in multilayer networks is discussed.