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A weighted planar stochastic lattice with scale-free, small-world and multifractal properties

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  • Mitra, Tushar
  • Hassan, Md. Kamrul

Abstract

We investigate a class of weighted planar stochastic lattice (WPSL1) created by random sequential nucleation of seed from which a crack is grown parallel to one of the sides of the chosen block and ceases to grow upon hitting another crack. It results in the partitioning of the square into contiguous and non-overlapping blocks. Interestingly, we find that the dynamics of WPSL1 is governed by infinitely many conservation laws and each of the conserved quantities, except the trivial conservation of total mass or area, is a multifractal measure. On the other hand, the dual of the lattice is a scale-free network as its degree distribution exhibits a power-law P(k)∼k−γ with γ=4. The network is also a small-world network as we find that (i) the total clustering coefficient C is high and independent of the network size and (ii) the mean geodesic path length grows logarithmically with N. Besides, the clustering coefficient Ck of the nodes which have degree k decreases exactly as 2/(k−1) revealing that it is also a nested hierarchical network.

Suggested Citation

  • Mitra, Tushar & Hassan, Md. Kamrul, 2022. "A weighted planar stochastic lattice with scale-free, small-world and multifractal properties," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921010109
    DOI: 10.1016/j.chaos.2021.111656
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    1. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    2. Cristopher Moore & M. E. J. Newman, 2000. "Exact Solution of Site and Bond Percolation on Small-World Networks," Working Papers 00-01-007, Santa Fe Institute.
    3. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    4. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    5. Flaviano Morone & Hernán A. Makse, 2015. "Correction: Corrigendum: Influence maximization in complex networks through optimal percolation," Nature, Nature, vol. 527(7579), pages 544-544, November.
    6. Flaviano Morone & Hernán A. Makse, 2015. "Influence maximization in complex networks through optimal percolation," Nature, Nature, vol. 524(7563), pages 65-68, August.
    7. Ciro Cattuto & Wouter Van den Broeck & Alain Barrat & Vittoria Colizza & Jean-François Pinton & Alessandro Vespignani, 2010. "Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks," PLOS ONE, Public Library of Science, vol. 5(7), pages 1-9, July.
    8. Hassan, Md. Kamrul & Islam, Liana & Haque, Syed Arefinul, 2017. "Degree distribution, rank-size distribution, and leadership persistence in mediation-driven attachment networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 23-30.
    Full references (including those not matched with items on IDEAS)

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