We consider a diffusion process on a graph  consisting  of two weakly connected complex networks.  Our diffusion model takes into account attractivenes of individual nodes in both graphs but neglects  interactions between moving particles. Using a time scale separation for   intra- an inter-network dynamcis we  found an effective equation for inter-network migration that is similar  to the Fick’s First Law. We estimated diffusion constants for a large class of complex networks and we derived an analytical  formula for the entropy production  in such systems.

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