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An exactly solvable model for the rewiring dynamics of weighted, directednetworks is introduced. Simulations indicate that the model exhibits two typesof condensation: (i) a phase in which, for each node, a finite fraction of itstotal out-strength condenses onto a single link; (ii) a phase in which a finitefraction of the total weight in the system is directed into a single node. Avirtue of the model is that its dynamics can be mapped onto those of azero-range process with many species of interacting particles -- an exactlysolvable model of particles hopping between the sites of a lattice. Thismapping, which is described in detail, guides the analysis of the steady stateof the network model and leads to theoretical predictions for the conditionsunder which the different types of condensation may be observed. A furtheradvantage of the mapping is that, by exploiting what is known about exactlysolvable generalisations of the zero-range process, one can infer a number ofgeneralisations of the network model and dynamics which remain exactlysolvable.Comment: 23 pages, 8 figure

Condensation transitions in a model for a directed network with weighted links