  An exactly solvable model for the rewiring dynamics of weighted, directed
networks is introduced. Simulations indicate that the model exhibits two types
of condensation: (i) a phase in which, for each node, a finite fraction of its
total out-strength condenses onto a single link; (ii) a phase in which a finite
fraction of the total weight in the system is directed into a single node. A
virtue of the model is that its dynamics can be mapped onto those of a
zero-range process with many species of interacting particles -- an exactly
solvable model of particles hopping between the sites of a lattice. This
mapping, which is described in detail, guides the analysis of the steady state
of the network model and leads to theoretical predictions for the conditions
under which the different types of condensation may be observed. A further
advantage of the mapping is that, by exploiting what is known about exactly
solvable generalisations of the zero-range process, one can infer a number of
generalisations of the network model and dynamics which remain exactly
solvable.
