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On the Exponential Ranking and Its Linear Counterpart

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Complex Networks & Their Applications X (COMPLEX NETWORKS 2021)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1072))

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Abstract

This paper deals with ranking algorithms for signed graphs. We analyze the algebraic properties of the exponential ranking algorithm and suggest an alternative ranking scheme that is close to the exponential ranking in several respects, but which also enjoys the property of being linear. We discuss the properties of the introduced scheme and present both algebraic and numerical evidence that it is indeed very close to the exponential ranking.

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Notes

  1. 1.

    Note that some papers (e.g., [21]) take a different notation, such that \(a_{ij}\) is defined as w(i, j). We have chosen to define the elements of \(\mathrm {A}\) according to (1) to later multiply \(\mathrm {A}\) with column instead of row vectors.

  2. 2.

    We are grateful to the reviewer for bringing this interpretation to our attention.

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Acknowledgments

The reported study was funded by the RFBR, project number 21-011-44058.

The authors are grateful to anonymous reviewers for their pointed remarks (especially considering the extremely short time allotted for reviewing).

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Authors and Affiliations

  1. Saint Petersburg State University, Saint Petersburg, Russia

    Dmitry Gromov & Elizaveta Evmenova

Authors
  1. Dmitry Gromov
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  2. Elizaveta Evmenova
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Corresponding author

Correspondence to Dmitry Gromov .

Editor information

Editors and Affiliations

  1. Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, Madrid, Madrid, Spain

    Rosa Maria Benito

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LIB, UFR Sciences et Techniques, University of Burgundy, Dijon, France

    Hocine Cherifi

  4. Grupo Interdisciplinar de Sistemas Complejos, Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Thomas J. Watson College of Engineering and Applied Science, Binghamton University, Binghamton, USA

    Luis M. Rocha

  6. Department of Chemical Engineering, Universitat Rovira i Virgili, Tarragona, Tarragona, Spain

    Marta Sales-Pardo

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Gromov, D., Evmenova, E. (2022). On the Exponential Ranking and Its Linear Counterpart. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol 1072. Springer, Cham. https://doi.org/10.1007/978-3-030-93409-5_22

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  • DOI: https://doi.org/10.1007/978-3-030-93409-5_22

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