Mapping And Application Analysis Of Weighted Complex Networks In Hyperbolic Space

In today’s big data era,as a mathematical model that can describe the relationship between individuals,complex networks have unique advantages for building a real system of big data networks.Complex network mapping aims to embed network data from a high-dimensional organizational structure into a low-dimensional measurement space.On the basis of preserving the original important characteristics of the network,it reveals the hidden features and properties of the network structure.This is useful for mining complex network characteristics and the application is of great significance.Research has found that embedding a complex network into a hyperbolic space can reveal the topological information presented by the complex network.Most of the current research on complex network mapping is to embed undirected and unweighted complex networks into hyperbolic space,but the actual complex systems still have weighted information.In response to this situation,this thesis considers a class of complex network systems with non-linear correlation s k~ηbetween node strength(weight sum)and degree,and proposes a weighted network generation model w PSO in hyperbolic space.Through the simulation analysis of the real network system,it is found that the w PSO generation network has a degree distribution and intensity distribution law similar to the real system,indicating that the generation model reveals the real complex network considered above,and specially when the weight value is all 1,the model is an undirected and unweighted PSO network generation model.On this basis,this thesis proposes a mapping algorithm HSS that embeds this kind of weight network into hyperbolic space.The algorithm firstly uses the hierarchical community structure information of the network,and proposes the community closeness index NCI based on the connections between communities and the common neighbor communities between them,so as to determine the order of the network communities in the hyperbolic space.The node similarity index WRA is constructed by using the strength between the node pairs and their common neighbors,which can reflect the relative angular distance of the node pair in the hyperbolic space,and then determine the hyperbolic angle coordinate after the node is mapped to the hyperbolic space.Experimental results show that the algorithm has excellent performance in mapping accuracy,network navigation and time complexity.Furthermore,inspired by the universal gravitation model,combined with the results of complex network hyperbolic mapping,the complex network link prediction is studied.Combined with the hyperbolic distance information between the node pair and their common neighbors in the hyperbolic space,a link prediction index HDR based on the idea of universal gravitation model is proposed,and the similarity performance of the index under different parameters is analyzed,and then a link prediction strategy based on the link prediction index HDR is proposed.The experimental results show that under this link prediction strategy,HDR has better prediction capabilities in both artificial and real networks compared with some existing excellent predictive indicators,especially for the network with low clustering coefficient,its prediction performance is more prominent.