  The topology of many real complex networks has been conjectured to be
embedded in hidden metric spaces, where distances between nodes encode their
likelihood of being connected. Besides of providing a natural geometrical
interpretation of their complex topologies, this hypothesis yields the recipe
for sustainable Internet's routing protocols, sheds light on the hierarchical
organization of biochemical pathways in cells, and allows for a rich
characterization of the evolution of international trade. We present empirical
evidence that this geometric interpretation also applies to the weighted
organisation of real complex networks. We introduce a very general and
versatile model and use it to quantify the level of coupling between their
topology, their weights, and an underlying metric space. Our model accurately
reproduces both their topology and their weights, and our results suggest that
the formation of connections and the assignment of their magnitude are ruled by
different processes.
