Research On Generalized Multi-fractal Dimension Analysis Method And Application For Large-scale Complex Networks

In recent years,the problem of feature analysis for large-scale complex networks has attracted extensive attention from researchers from academia and industry.Among them,the study of self-similar problems in complex networks is of great significance for describing network structure characteristics and revealing network evolution rules.It has gradually become a research hotspot in this field,and a theoretical analysis method based on fractal theory has been formed.However,in the study of self-similarity of complex networks,only the fractal dimension is used,which is not enough to accurately describe the self-similarity characteristics of complex networks.In view of this problem,multifractal dimension is an important index to describe the self-similarity of complex networks from different dimensions on the basis of fractal analysis,and has irreplaceable advantages in describing the structural characteristics of complex networks.At present,in the field of multifractal analysis for complex networks,the sandbox algorithm uses statistical methods to approximate the self-similarity of complex networks.Compared with the multifractal analysis methods based on box counting method and box burning method,it has obvious technical advantages.However,this algorithm has high computational complexity,and it still has certain difficulties when applied to self-similarity analysis of large-scale complex networks.Therefore,how to reduce the computational complexity of the sandbox algorithm,improve its computational efficiency,and further expand the scope of application of the sandbox algorithm is one of the important issues that need to be solved in this field.Based on the sandbox algorithm,this paper analyzes and studies the technical bottlenecks that limit its computational efficiency,and proposes a targeted and improved sandbox algorithm.According to the characteristics of the sandbox algorithm,a technical solution using compressed sparse matrix and breadth-first search to replace the shortest path matrix is proposed,thereby reducing the computational complexity of the sandbox algorithm.And through the(u,v)-flower theoretical network model,the analysis accuracy and calculation efficiency of the improved sandbox algorithm are analyzed and verified.Finally,based on the improved sandbox algorithm proposed in this study,the self-similarity of actual large-scale complex networks(including brain neural networks,social networks,tagging networks,citation networks,etc.)are analyzed and studied.