Link Prediction And Analysis Of Complex Network Under Hyperbolic Mapping

Various complex systems in the real world can be characterized as networks,so complex network science has become a powerful tool for further revealing mechanisms and understanding real phenomena.Link prediction,as the main research content of complex networks,has attracted great attention from researchers in different fields.Research on link prediction can theoretically help to understand the mechanism of information dissemination and information diffusion.In the actual field,it can recommend different projects to customers or effectively guide complex experiments through known information to reduce the cost of exploring unknowns.Therefore,the research of complex network link prediction is of great significance.Recent studies have shown that many real networks exhibit hyperbolic characteristics during airworthiness and evolution,which provides a new perspective for the study of complex network link prediction.Hyperbolic geometry helps people understand the hidden structure and dynamic characteristics of complex networks.Obtaining and analyzing the hyperbolic geometry of the network requires the hyperbolic mapping method to embed the network into the hyperbolic space and quantify it.Existing network hyperbolic mapping methods are mainly based on global maximum likelihood functions or machine learning.When dealing with large-scale networks,they are often limited by runtime or memory space.In order to solve this problem,considering the characteristics of complex networks with community structure and self-similarity,we first proposed a community compactness index CNES(Common Neighbor's Edge Strength based Index)..Then a linear time complexity hyperbolic mapping algorithm FM(Fast Mapping Algorithm)based on a layered community structure is analyzed and explored.Furthermore,a local maximum likelihood function based on network node degree and community is proposed.The local maximum likelihood function replaces the global maximum likelihood function to quantify the accuracy of the hyperbolic angle coordinates of the network mapping.Based on the FM algorithm,a hyperbolic mapping algorithm called FMLE is proposed.It used the proposed local maximum likelihood function to optimize the hyperbolic angle coordinates of the nodes and a balance of algorithm mapping accuracy and time is achieved.Using the hyperbolic geometry of the network,this paper analyzes the link prediction from the perspective of the network structure.Considering the hyperbolic coordinates of the network are a manifestation of the comprehensive trade-off between node popularity and similarity,we incorporate effective topology information and propose a link prediction index(HC)and a link prediction algorithm(HC Algorithm)based on the network hyperbolicity and clustering coefficient which improve link prediction performance.Experiments show that the HC index effectively characterizes the link similarity.Above a certain network mapping accuracy,the HC algorithm is basically not affected by the accuracy of the hyperbolic mapping method,and it is robust.Compared with mainstream link prediction algorithms,It also has extremely high link prediction accuracy.