  Networked structures arise in a wide array of different contexts such as
technological and transportation infrastructures, social phenomena, and
biological systems. These highly interconnected systems have recently been the
focus of a great deal of attention that has uncovered and characterized their
topological complexity. Along with a complex topological structure, real
networks display a large heterogeneity in the capacity and intensity of the
connections. These features, however, have mainly not been considered in past
studies where links are usually represented as binary states, i.e. either
present or absent. Here, we study the scientific collaboration network and the
world-wide air-transportation network, which are representative examples of
social and large infrastructure systems, respectively. In both cases it is
possible to assign to each edge of the graph a weight proportional to the
intensity or capacity of the connections among the various elements of the
network. We define new appropriate metrics combining weighted and topological
observables that enable us to characterize the complex statistical properties
and heterogeneity of the actual strength of edges and vertices. This
information allows us to investigate for the first time the correlations among
weighted quantities and the underlying topological structure of the network.
These results provide a better description of the hierarchies and
organizational principles at the basis of the architecture of weighted
networks.
