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Detection of hubs in complex networks by the Laplacian matrix

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Abstract

We propose a definition of hub in complex networks by using the eigenvectors of the Laplacian matrix, and suggest a method of detecting hubs. The proposed definition provides a different concept from the classical measures such as the centrality or degree. Also, a method of determining the number of hubs is suggested using a scree plot. Illustrative examples based on artificial data sets and real data sets are given.

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Authors and Affiliations

  1. Statistics Research Institute, Daejeon, Korea

    Younghee Hong

  2. Daegu Gyeongbuk Institute of Science and Technology, Daegu, Korea

    Iksoo Chang

  3. Pusan National University, Busan, Korea

    Choongrak Kim

Authors
  1. Younghee Hong
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  2. Iksoo Chang
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  3. Choongrak Kim
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Correspondence to Choongrak Kim.

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This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No.2019R1A2C1007193 to C. Kim) and the Ministry of Science, Technology and ICT(NRF-2017R1E1A1A03070854 to I.Chang).

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Hong, Y., Chang, I. & Kim, C. Detection of hubs in complex networks by the Laplacian matrix. J. Korean Stat. Soc. 50, 431–446 (2021). https://doi.org/10.1007/s42952-020-00087-0

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  • DOI: https://doi.org/10.1007/s42952-020-00087-0

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