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Fellow Travelers Phenomenon Present in Real-World Networks

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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

We investigate a metric parameter “Leanness” of graphs which is a formalization of a well-known Fellow Travelers Property present in some metric spaces. Given a graph \(G=(V,E)\), the leanness of G is the smallest \(\lambda \) such that, for every pair of vertices \(x,y\in V\), all shortest (x, y)-paths stay within distance \(\lambda \) from each other. We show that this parameter is bounded for many structured graph classes and is small for many real-world networks. We present efficient algorithms to compute or estimate this parameter and evaluate the performance of our algorithms on a number of real-world networks.

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Notes

  1. 1.

    This is known (see, e.g., [6]) also under the name \(\lambda \)-thin interval, but to differentiate graph thinness parameter based on the thinness of geodesic triangles from the graph thinness based on thinness of intervals, we use here the word lean.

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Author information

Authors and Affiliations

  1. Duhok Polytechnic University, Duhok, Kurdistan Region, Iraq

    Abdulhakeem O. Mohammed

  2. Computer Science Department, Kent State University, Kent, USA

    Feodor F. Dragan

  3. Department of Mathematical and Computational Sciences, The College of Wooster, Wooster, USA

    Heather M. Guarnera

Authors
  1. Abdulhakeem O. Mohammed
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  2. Feodor F. Dragan
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  3. Heather M. Guarnera
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Corresponding author

Correspondence to Abdulhakeem O. Mohammed .

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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Mohammed, A.O., Dragan, F.F., Guarnera, H.M. (2022). Fellow Travelers Phenomenon Present in Real-World Networks. 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_17

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  • DOI: https://doi.org/10.1007/978-3-030-93409-5_17

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  • Online ISBN: 978-3-030-93409-5

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