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Geometry of minimum spanning trees on scale-free networks

Author

Listed:
  • Szabó, Gábor J.
  • Alava, Mikko
  • Kertész, János

Abstract

The minimum spanning trees on scale-free graphs are shown to be scale-free as well, in the presence of random edge weights. The probability distribution of the weights on the tree differs from regular lattices reflecting the typically short distances (small-world property). We consider also the trees in the absence of such randomness and the ensuing massive degeneracy, which is analyzed with graph theoretical arguments.

Suggested Citation

  • Szabó, Gábor J. & Alava, Mikko & Kertész, János, 2003. "Geometry of minimum spanning trees on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 31-36.
    • Handle: RePEc:eee:phsmap:v:330:y:2003:i:1:p:31-36
    DOI: 10.1016/j.physa.2003.08.031
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    Cited by:

    1. Djauhari, Maman Abdurachman & Gan, Siew Lee, 2015. "Optimality problem of network topology in stocks market analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 108-114.
    2. Milena Oehlers & Benjamin Fabian, 2021. "Graph Metrics for Network Robustness—A Survey," Mathematics, MDPI, vol. 9(8), pages 1-48, April.
    3. Huanshen Jia & Guona Hu & Haixing Zhao, 2014. "Topological Properties of a 3-Regular Small World Network," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-4, April.

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