  Generalising the concept of Bell nonlocality to networks leads to novel forms
of correlations, the characterization of which is however challenging. Here we
investigate constraints on correlations in networks under the two natural
assumptions of no-signaling and independence of the sources. We consider the
``triangle network'', and derive strong constraints on correlations even though
the parties receive no input, i.e. each party performs a fixed measurement. We
show that some of these constraints are tight, by constructing explicit local
models (i.e. where sources distribute classical variables) that can saturate
them. However, we also observe that other constraints can apparently not be
saturated by local models, which opens the possibility of having nonlocal (but
non-signaling) correlations in the triangle network.
