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Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

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Abstract

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as N → ∞. For the even dimensions of space, d = 2, 4, 6,..., the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.

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Authors and Affiliations

  1. BiBoS, University Bielefeld, Postfach 100131, D-33501, Bielefeld, Germany

    D. Volchenkov & Ph. Blanchard

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  1. D. Volchenkov
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  2. Ph. Blanchard
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Correspondence to D. Volchenkov.

Additional information

PACS codes: 87.15.Vv, 89.75.Hc, 89.75.Fb

The Alexander von Humboldt Research Fellow at the BiBoS Research Center

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Volchenkov, D., Blanchard, P. Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs. J Stat Phys 127, 677–697 (2007). https://doi.org/10.1007/s10955-007-9313-1

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  • DOI: https://doi.org/10.1007/s10955-007-9313-1

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