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We suggest a minimalistic model for directed networks and suggest an application to injection and merging of magnetic field lines. We obtain a network of connected donor and acceptor vertices with degree distribution 1/s 2, and with dynamical reconnection events of size Δs occurring with frequency that scales as 1/Δs 3. This suggests that the model is in the same universality class as the model with annihilation for self-organization in the solar atmosphere suggested by Hughes et al.(Phys. Rev. Lett. 90 (2003) 131101).