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Using deterministic self-avoiding walks as a small-world metric on Watts–Strogatz networks

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  • Merenda, João V.B.S.
  • Bruno, Odemir M.

Abstract

The Watts–Strogatz model (WS) has been demonstrated to effectively describe real-world networks due to its ability to reproduce the small-world properties commonly observed in a variety of systems, including social networks, computer networks, biochemical reactions, and neural networks. As the presence of small-world properties is a prevalent characteristic in many real-world networks, the measurement of ”small-worldness” has become a crucial metric in the field of network science, leading to the development of various methods for its assessment over the past two decades. In contrast, the deterministic tourist walk (DTW) method has emerged as a prominent technique for texture analysis and network classification. In this paper, we propose the use of a modified version of the DTW method to classify networks into three categories: regular networks, random networks, and small-world networks. Additionally, we construct a small-world metric, denoted by the coefficient γ, from the DTW method. Results indicate that the proposed method demonstrates excellent performance in the task of network classification, achieving over 90% accuracy. Furthermore, the results obtained using the coefficient γ on real-world networks provide evidence that the proposed method effectively serves as a satisfactory small-world metric.

Suggested Citation

  • Merenda, João V.B.S. & Bruno, Odemir M., 2023. "Using deterministic self-avoiding walks as a small-world metric on Watts–Strogatz networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
  • Handle: RePEc:eee:phsmap:v:621:y:2023:i:c:s0378437123002686
    DOI: 10.1016/j.physa.2023.128713
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    References listed on IDEAS

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    1. Robert L. Axtell, 2000. "Effect of Interaction Topology and Activation Regime in Several Multi-Agent Systems," Working Papers 00-07-039, Santa Fe Institute.
    2. Scabini, Leonardo F.S. & Ribas, Lucas C. & Neiva, Mariane B. & Junior, Altamir G.B. & Farfán, Alex J.F. & Bruno, Odemir M., 2021. "Social interaction layers in complex networks for the dynamical epidemic modeling of COVID-19 in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    3. Terçariol, César Augusto Sangaletti & González, Rodrigo Silva & Oliveira, Wilnice Tavares Reis & Martinez, Alexandre Souto, 2007. "Deterministic and random partially self-avoiding walks in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(2), pages 678-680.
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