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Growing Homophilic Networks Are Natural Navigable Small Worlds

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  • Yury A Malkov
  • Alexander Ponomarenko

Abstract

Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of navigation properties remained unknown. We show that navigability can be achieved by using only two ingredients present in the majority of networks: network growth and local homophily, giving a persuasive answer how the navigation appears in real-life networks. A very simple algorithm produces hierarchical self-similar optimally wired navigable small world networks with exponential degree distribution by using only local information. Adding preferential attachment produces a scale-free network which has shorter greedy paths, but worse (power law) scaling of the information extraction locality (algorithmic complexity of a search). Introducing saturation of the preferential attachment leads to truncated scale-free degree distribution that offers a good tradeoff between these parameters and can be useful for practical applications. Several features of the model are observed in real-life networks, in particular in the brain neural networks, supporting the earlier suggestions that they are navigable.

Suggested Citation

  • Yury A Malkov & Alexander Ponomarenko, 2016. "Growing Homophilic Networks Are Natural Navigable Small Worlds," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-14, June.
  • Handle: RePEc:plo:pone00:0158162
    DOI: 10.1371/journal.pone.0158162
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    References listed on IDEAS

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    1. Jon M. Kleinberg, 2000. "Navigation in a small world," Nature, Nature, vol. 406(6798), pages 845-845, August.
    2. Huang, Wei & Chen, Shengyong & Wang, Wanliang, 2014. "Navigation in spatial networks: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 132-154.
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    Cited by:

    1. Shandeepa Wickramasinghe & Onyekachukwu Onyerikwu & Jie Sun & Daniel ben-Avraham, 2018. "Modeling Spatial Social Complex Networks for Dynamical Processes," Complexity, Hindawi, vol. 2018, pages 1-12, February.

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