Link Prediction And Core Percolation On Complex Networks

As an extensive material form in the real world,network has become an important means to study complex systems.With the deep understanding of the network structure,Static simple network exposes its inherent limitations.In many natural and industrial systems,the complex and diverse interaction of time-varying characteristic and other types among entities,shows the 'multilayer' features.The interaction between the layers and the connectivity in the layers together lead to its complex characteristics.Compared to the traditional networks,multilayer network model is a more accurate characterization of the real-world networks.In order to further understand the complex systems,studying and characterizing multilayer networks become a new breakthrough.In this paper,we focus on network topology and network dynamics process,from the perspective of application and theory respectively.We first review the development of network science,summarize the research status at home and abroad,and briefly introduce the basic network metrics and related theoretical knowledge,including classical link prediction algorithm and percolation theory.In the study of network link prediction problem,we propose a degree-related clustering coefficientto resist the bias caused by the missing links in the network,which leads to the misjudgement of the nodes clustering ability.Combining with the information of path,we design a link prediction algorithm DCP based on this coefficient.Compared with the classical algorithm based on common neighbors,the proposed algorithm obtainsgood predictive performance in 12 empirical networks.Meanwhile,the algorithm parameter setting and stability analysis in the paper also improve the application efficiency of the algorithm.As for multilayer networks,we take multiplex as the research object.As an empirical study,we first analyze the topology characteristic of a collaboration-citation network with 38593 authors.Secondly,a pruning algorithm in single-layer network is extended to multilayer network,using rate equation method,we study the the evolution of degree distribution during the pruning process in Poisson distribution,exponential distribution,pure power law distribution and static model networks.The numerical results obtaining by solving equations are in good agreement with the simulation results in the random networks,which verifies the correctness of the equations.The results show that,unlike single networks,core percolation in multiplex network exhibits discontinuous phase transition behavior.At last,we give the rate equation of the multiplex network with arbitrary degree distribution.