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Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

D. Volchenkov·Ph. Blanchard
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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 $N\to\infty.$ 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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D. Volchenkov, Ph. Blanchard. 2006-12-08. Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs. https://doi.org/10.1007/s10955-007-9313-1

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