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Finding shortest and nearly shortest path nodes in large substantially incomplete networks by hyperbolic mapping

Author

Listed:
  • Maksim Kitsak

    (Delft University of Technology
    Northeastern University)

  • Alexander Ganin

    (University of Virginia, Department of Systems and Information Engineering
    U.S. Army Engineer Research and Development Center, Contractor)

  • Ahmed Elmokashfi

    (Simula Metropolitan Center for Digital Engineering)

  • Hongzhu Cui

    (Worcester Polytechnic Institute
    Columbia University Medical Center)

  • Daniel A. Eisenberg

    (Naval Postgraduate School)

  • David L. Alderson

    (Naval Postgraduate School)

  • Dmitry Korkin

    (Worcester Polytechnic Institute
    Worcester Polytechnic Institute
    Worcester Polytechnic Institute)

  • Igor Linkov

    (Environmental Laboratory)

Abstract

Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Computing shortest paths is a straightforward task when the network of interest is fully known, and there are a plethora of computational algorithms for this purpose. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions and the Internet at the autonomous system level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks, where numbers of missing links exceed those of observable links. We demonstrate the utility of latent-geometric path finding in problems of cellular pathway reconstruction and communication security.

Suggested Citation

  • Maksim Kitsak & Alexander Ganin & Ahmed Elmokashfi & Hongzhu Cui & Daniel A. Eisenberg & David L. Alderson & Dmitry Korkin & Igor Linkov, 2023. "Finding shortest and nearly shortest path nodes in large substantially incomplete networks by hyperbolic mapping," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
  • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-022-35181-w
    DOI: 10.1038/s41467-022-35181-w
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    References listed on IDEAS

    as
    1. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    2. Fragkiskos Papadopoulos & Maksim Kitsak & M. Ángeles Serrano & Marián Boguñá & Dmitri Krioukov, 2012. "Popularity versus similarity in growing networks," Nature, Nature, vol. 489(7417), pages 537-540, September.
    3. Marián Boguñá & Fragkiskos Papadopoulos & Dmitri Krioukov, 2010. "Sustaining the Internet with hyperbolic mapping," Nature Communications, Nature, vol. 1(1), pages 1-8, December.
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    Cited by:

    1. Gregor Svindland & Alexander Vo{ss}, 2023. "Decision-Making Frameworks for Network Resilience -- Managing and Mitigating Systemic (Cyber) Risk," Papers 2312.13884, arXiv.org, revised Oct 2024.

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