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SP: Shell-Based Perturbation Approach to Localize Principal Eigen Vector of a Network Adjacency Matrix

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Intelligent Systems (ICMIB 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 728))

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Abstract

Recently, research in the spread of information is found to be a crucial domain in the field of social network analysis. Understanding information spreadability and controllability are the two aspects of the same study. One of the important network parameters, the Inverse Participation Ratio (IPR) of a network adjacency matrix can measure the state of information localization. Higher the value of IPR, the higher the state of localization. This paper proposes a new perturbation approach based on k-shell decomposition to meet the optimal IPR. The proposed Shell-based Perturbation (SP) approach is compared with one of the state-of-the-art approaches: Random Perturbation (RP). The result confirms the superior performance of the proposed SP approach over the existing RP approach.

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References

  1. Dwivedi SK, Sarkar C, Jalan S (2015) Optimization of synchronizability in multiplex networks. EPL (Europhys Lett) 111(1):10005

    Article  Google Scholar 

  2. Dwivedi SK, Jalan S (2014) Emergence of clustering: role of inhibition. Phys Rev E 90(3):032803

    Article  Google Scholar 

  3. Pradhan P, Yadav A, Dwivedi SK, Jalan S (2017) Optimized evolution of networks for principal eigenvector localization. Phys Rev E 96(2):022312

    Article  Google Scholar 

  4. Kitsak M, Gallos LK, Havlin S, Liljeros F, Muchnik L, Stanley HE, Makse HA (2010) Identification of influential spreaders in complex networks. Nat Phys 6(11):888–893

    Article  Google Scholar 

  5. Newman MEJ (2010) Networks: an introduction. Oxford University Press, New York

    Book  MATH  Google Scholar 

  6. Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pp 137–146

    Google Scholar 

  7. Pradhan P, Jalan S (2020) From spectra to localized networks: a reverse engineering approach. IEEE Trans Netw Sci Eng 7(4):3008–3017

    Article  MathSciNet  Google Scholar 

  8. Mohapatra D (2021) Jaccard guided perturbation for eigenvector localization. N Gener Comput 39(1):159–179

    Article  Google Scholar 

  9. Goltsev AV, Dorogovtsev SN, Oliveira JG, Mendes JF (2012) Localization and spreading of diseases in complex networks. Phys Rev Lett 109(12):128702

    Article  Google Scholar 

  10. Pradhan P, Angeliya CU, Jalan S (2020) Principal eigenvector localization and centrality in networks: revisited. Physica A 554:124169

    Article  MATH  Google Scholar 

  11. Forrow A, Woodhouse FG, Dunkel J (2018) Functional control of network dynamics using designed Laplacian spectra. Phys Rev X 8(4):041043

    Google Scholar 

  12. Rings T, Bröhl T, Lehnertz K (2022) Network structure from a characterization of interactions in complex systems. Sci Rep 12(1):1–19

    Article  Google Scholar 

  13. Carmi S, Havlin S, Kirkpatrick S, Shavitt Y, Shir E (2007) A model of Internet topology using k-shell decomposition. Proc Natl Acad Sci 104(27):11150–11154

    Article  Google Scholar 

  14. Elsner L, Van den Driessche P (2001) Modifying the power method in max algebra. Linear Algebra Appl 332:3–13

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang Z, Zhao Y, Xi J, Du C (2016) Fast ranking influential nodes in complex networks using a k-shell iteration factor. Physica A 461:171–181

    Article  Google Scholar 

  16. Lehnertz K (2023) Ordinal methods for a characterization of evolving functional brain networks. Chaos Interdisc J Nonlinear Sci 33(2):022101

    Google Scholar 

  17. Briggs JK, Kravets V, Dwulet JM, Albers DJ, Benninger RK (2022) Beta-cell metabolic activity rather than gap junction structure dictates subpopulations in the islet functional network. bioRxiv, 2022-02

    Google Scholar 

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Acknowledgements

We acknowledge the OSHEC, Odisha, India for providing financial support under the Odisha University Research and Innovation Incentivization Plan (OURIIP) with Grant Number 21SF/CS/2019.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Parala Maharaja Engineering College, Berhampur, 761003, Odisha, India

    Baishnobi Dash & Debasis Mohapatra

Authors
  1. Baishnobi Dash
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  2. Debasis Mohapatra
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Corresponding author

Correspondence to Debasis Mohapatra .

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Editors and Affiliations

  1. School of Computer and Information Sciences, University of Hyderabad, Hyderabad, Telangana, India

    Siba K. Udgata

  2. Department of Computer Science and Engineering, Indira Gandhi Institute of Technology, Dhenkanal, Odisha, India

    Srinivas Sethi

  3. Department of Computer Science, University of Eastern Finland, Kuopio, Finland

    Xiao-Zhi Gao

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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Dash, B., Mohapatra, D. (2024). SP: Shell-Based Perturbation Approach to Localize Principal Eigen Vector of a Network Adjacency Matrix. In: Udgata, S.K., Sethi, S., Gao, XZ. (eds) Intelligent Systems. ICMIB 2023. Lecture Notes in Networks and Systems, vol 728. Springer, Singapore. https://doi.org/10.1007/978-981-99-3932-9_32

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  • DOI: https://doi.org/10.1007/978-981-99-3932-9_32

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-3931-2

  • Online ISBN: 978-981-99-3932-9

  • eBook Packages: EngineeringEngineering (R0)

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