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Visibility in the topology of complex networks

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  • Tsiotas, Dimitrios
  • Charakopoulos, Avraam

Abstract

Taking its inspiration from the visibility algorithm, which was proposed by Lacasa et al. (2008) to convert a time-series into a complex network, this paper develops and proposes a novel expansion of this algorithm that allows generating a visibility graph from a complex network instead of a time-series that is currently applicable. The purpose of this approach is to apply the idea of visibility from the field of time-series to complex networks in order to interpret the network topology as a landscape. Visibility in complex networks is a multivariate property producing an associated visibility graph that maps the ability of a node “to see” other nodes in the network that lie beyond the range of its neighborhood, in terms of a control-attribute. Within this context, this paper examines the visibility topology produced by connectivity (degree) in comparison with the original (source) network, in order to detect what patterns or forces describe the mechanism under which a network is converted to a visibility graph. The overall analysis shows that visibility is a property that increases the connectivity in networks, it may contribute to pattern recognition (among which the detection of the scale-free topology) and it is worth to be applied to complex networks in order to reveal the potential of signal processing beyond the range of its neighborhood. Generally, this paper promotes interdisciplinary research in complex networks providing new insights to network science.

Suggested Citation

  • Tsiotas, Dimitrios & Charakopoulos, Avraam, 2018. "Visibility in the topology of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 280-292.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:280-292
    DOI: 10.1016/j.physa.2018.03.055
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    References listed on IDEAS

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    1. César Ducruet & Laurent Beauguitte, 2014. "Spatial Science and Network Science: Review and Outcomes of a Complex Relationship," Networks and Spatial Economics, Springer, vol. 14(3), pages 297-316, December.
    2. Liu, Chuang & Zhou, Wei-Xing & Yuan, Wei-Kang, 2010. "Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2675-2681.
    3. Yang, Yue & Yang, Huijie, 2008. "Complex network-based time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1381-1386.
    4. BRANDES, ULRIK & ROBINS, GARRY & McCRANIE, ANN & WASSERMAN, STANLEY, 2013. "What is network science?," Network Science, Cambridge University Press, vol. 1(01), pages 1-15, April.
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    Cited by:

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    3. Tsiotas, Dimitrios & Niavis, Spyros & Sdrolias, Labros, 2018. "Operational and geographical dynamics of ports in the topology of cruise networks: The case of Mediterranean," Journal of Transport Geography, Elsevier, vol. 72(C), pages 23-35.

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