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Mean Hitting Time of Q-subdivision Complex Networks

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Complex Networks and Their Applications XI (COMPLEX NETWORKS 2016 2022)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1078))

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Abstract

The Mean Hitting Time is a fundamental structural measure of random walks on networks with many applications ranging from epidemic diffusion on networks to fluctuations in stock prices. It measures the mean expected time for a random walker to reach all the source-destination pair nodes in the network. Previous research shows that it scales linearly with the network size for small-world sparse networks. Here, we calculate the Mean Hitting Time for large real-work complex networks and investigate how it scales with the q-subdivision operation used to grow the network. Indeed, this operation is essential in modeling realistic networks with small-world, scale-free and fractal characteristics. We use the Eigenvalues and eigenvectors of the normalized adjacency matrix of the initial network G to calculate the Hitting Time \(T_{ij}\) between nodes i and j. We consider two complex real-world networks to analyze the evolution of the Mean Hitting Time as the networks grow with the q-subdivision. Results show that the Mean Hitting Time increases linearly with the value of q. This work provides insight into the design of realistic networks with small Mean Hitting Time.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology Delhi, New Delhi, India

    Pankaj Kumar, Anurag Singh & Ajay K. Sharma

  2. University of Burgundy, Dijon, France

    Hocine Cherifi

Authors
  1. Pankaj Kumar
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  2. Anurag Singh
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  3. Ajay K. Sharma
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  4. Hocine Cherifi
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Corresponding author

Correspondence to Pankaj Kumar .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon, France

    Hocine Cherifi

  2. Dipartimento di Fisica e Chimica—Emilio Segrè, Università degli Studi Palermo, Palermo, Italy

    Rosario Nunzio Mantegna

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

    Luis M. Rocha

  4. IUT Lumière—Université Lyon 2, University of Lyon, Bron, France

    Chantal Cherifi

  5. Dipartimento di Fisica e Chimica—Emilio Segrè, Università degli Studi Palermo, Palermo, Italy

    Salvatore Micciche

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Kumar, P., Singh, A., Sharma, A.K., Cherifi, H. (2023). Mean Hitting Time of Q-subdivision Complex Networks. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-031-21131-7_28

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  • DOI: https://doi.org/10.1007/978-3-031-21131-7_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21130-0

  • Online ISBN: 978-3-031-21131-7

  • eBook Packages: EngineeringEngineering (R0)

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