  Large-scale multisource networks have been employed to overcome the practical
constraints that entangled systems are difficult to faithfully transmit over
large distance or store in long time. However, a full characterization of the
multipartite nonlocality of these networks remains out of reach, mainly due to
the complexity of multipartite causal models. In this paper, we propose a
general framework of Bayesian networks to reveal connections among different
causal structures. The present model implies a special star-convex set of
non-signaling correlations from multisource networks that allows constructing
polynomial-time algorithm for solving the compatibility problem of a given
correlation distribution and a fixed causal network. It is then used to
classify the nonlocality originated from the standard entanglement swapping of
tripartite networks. Our model provides a unified device-independent
information processing method for exploring the practical security against
non-signaling eavesdroppers on multisource quantum networks.
