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Complex Networks and Symmetry I: A Review

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  • Diego Garlaschelli
  • Franco Ruzzenenti
  • Riccardo Basosi

Abstract

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less developed. We argue that real networks, as any entity characterized by imperfections or errors, necessarily require a stochastic notion of invariance. We therefore propose a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective. The results discussed here and in a companion paper show that stochastic symmetry highlights the most informative topological properties of real networks, even in noisy situations unaccessible to exact techniques.

Suggested Citation

  • Diego Garlaschelli & Franco Ruzzenenti & Riccardo Basosi, 2010. "Complex Networks and Symmetry I: A Review," Papers 1006.3923, arXiv.org, revised Sep 2010.
    • Handle: RePEc:arx:papers:1006.3923
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    File URL: http://arxiv.org/pdf/1006.3923
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    Cited by:

    1. Ruzzenenti, Franco & Basosi, Riccardo, 2017. "Modelling the rebound effect with network theory: An insight into the European freight transport sector," Energy, Elsevier, vol. 118(C), pages 272-283.
    2. Smith, Dallas & Webb, Benjamin, 2019. "Hidden symmetries in real and theoretical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 855-867.

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