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∞. 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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