### Abstract

I will introduce a model for the rewiring dynamics of a directed, weighted network which undergoes two kinds of condensation: (i) a phase in which, for each node, a finite fraction of its 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. I will describe how the model can be mapped onto an exactly solvable zero-range process with many species of interacting particles and illustrate how one can exploit the mapping in order to obtain theoretical predictions for the conditions under which the different types of condensation are observed.