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

doi:10.1088/1674-1056/ac6867

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: lupengli88@163.com;chenwei_9711@163.com

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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