Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

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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