Weighted Sparse N-β And λ-β Models And Their Applications In Journal Citation Networks

With the development of science and technology,data in the form of the network can be seen everywhere.How to mine core nodes among massive nodes has gradually become one of the key research directions.Various methods have been applied to identify core nodes with corresponding evaluation indicators in different application scenarios.However,there are few parameter models for analyzing weighted networks.Therefore,based on the sparse β model（SβM）,we propose two statistical models for mining and sorting core nodes in the undirected weighted network-weighted sparse N-β model（WSN-βM）and weighted sparse λ-β model（WSλ-βM）.WSN-βM and WSλ-βM grasp the overall characteristics of the network from different scales,and then mine the core nodes and rank them.In the theoretical part,we prove the properties of each model from three aspects:order preservation,difference and stability.Based on the characteristics of WSN-βM and WSλ-βM,we show that both of them are order-preserving and then generalize the method of SβM to accelerate the process of parameter estimation,which solves the combinatorial calculation problem caused by the model with l0-norm constraints and ensures the solvability of the model.By analyzing the minimum threshold of the parameters of the two models,we get the difference in the strength between the core nodes and common nodes,which illustrates the rationality of the model structure.As for stability,we analyze the excess risk of parameter estimation and obtain their upper bound of probability.The experimental results of numerical simulation of these models have been displayed on three levels:the accuracy of core node identification,the estimation error of global feature and local feature.We show that both models perform well under different parameter configurations in all aspects.Since the journal ranking based on citation network data has been widely concerned,this paper crawled citation data of economics journals in the Chinese Social Sciences Citation Index（CSSCI）as examples for case analysis.According to the common problems of journal ranking,we conduct citation analysis and network construction on journal data.Focusing on cross references between journals,we use W SN-βM and WSλ-βM to mine authoritative journals.The results show that the two models are effective in mining authoritative journals and potential journals.