  Quantum nonlocality can be demonstrated without inputs (i.e. each party using
a fixed measurement setting) in a network with independent sources. Here we
consider this effect on ring networks, and show that the underlying quantum
strategy can be partially characterized, or self-tested, from observed
correlations. Applying these results to the triangle network allows us to show
that the nonlocal distribution of Renou et al. [Phys. Rev. Lett. 123, 140401
(2019)] requires that (i) all sources produce a minimal amount of entanglement,
(ii) all local measurements are entangled, and (iii) each local outcome
features a minimal entropy. Hence we show that the triangle network allows for
genuine network quantum nonlocality and certifiable randomness.
