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Community Structure and Multi-Modal Oscillations in Complex Networks

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  • Henry Dorrian
  • Jon Borresen
  • Martyn Amos

Abstract

In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.

Suggested Citation

  • Henry Dorrian & Jon Borresen & Martyn Amos, 2013. "Community Structure and Multi-Modal Oscillations in Complex Networks," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.
    • Handle: RePEc:plo:pone00:0075569
    DOI: 10.1371/journal.pone.0075569
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    References listed on IDEAS

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    1. Rodrigo Aldecoa & Ignacio Marín, 2011. "Deciphering Network Community Structure by Surprise," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-8, September.
    2. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    3. Wang, Xiao-Hua & Jiao, Li-Cheng & Wu, Jian-She, 2009. "Extracting hierarchical organization of complex networks by dynamics towards synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2975-2986.
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