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Chin. Phys. B, 2023, Vol. 32(1): 018903    DOI: 10.1088/1674-1056/ac6867

Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding

Pengli Lu(卢鹏丽) and Wei Chen(陈玮)
School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, China
Abstract  Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks, solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.
Keywords:  complex networks      centrality      joint nonnegative matrix factorization      graph embedding      smoothness strategy  
Received:  03 March 2022      Revised:  01 April 2022      Accepted manuscript online:  20 April 2022
PACS:  89.75.-k (Complex systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 62162040 and 11861045).
Corresponding Authors:  Pengli Lu, Wei Chen     E-mail:;

Cite this article: 

Pengli Lu(卢鹏丽) and Wei Chen(陈玮) Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding 2023 Chin. Phys. B 32 018903

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