Random graphs are useful mathematical models to study complex systems.
In particular, the use of weighted random networks allows to handle a high level of information concerning how the elements of the system interact and in which degree these interactions take place. In this talk, we focus on how weighted networks can be employed to obtain information on human activity. The recent availability of big size databases on several aspects of our daily life thanks to the Internet is an important asset for social sciences whose understanding and characterization requires new mathematical and technological approaches. From publication patterns to web navigation, we will show how the use of weighted networks permits the quantitative characterization of the tendency of people to keep the same collaborators or visiting the same sites. We compare, as well, the empirical results with models proposed for the generation of this type of graphs.