Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

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.

21 pages, 2 figures included

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• Modelling Complex Networks: Cameo Graphs And Transport Processes