  In a quantum network, distant observers sharing physical resources emitted by
independent sources can establish strong correlations, which defy any classical
explanation in terms of local variables. We discuss the characterization of
nonlocal correlations in such a situation, when compared to those that can be
generated in networks distributing independent local variables. We present an
iterative procedure for constructing Bell inequalities tailored for networks:
starting from a given network, and a corresponding Bell inequality, our
technique provides new Bell inequalities for a more complex network, involving
one additional source and one additional observer. The relevance of our method
is illustrated on a variety of networks, for which we demonstrate significant
quantum violations.
