  Quantum correlations arising in Bell experiments, involving a physical source
that emits a quantum state to a number of observers, have been intensively
studied over the last decades. Much less is known about the nature of quantum
correlations arising in network structures beyond the Bell experiments. Such
networks can involve many independent sources emitting states to observers in
accordance with the network configuration. Here, we will study classical and
quantum correlations in a family of networks which can be regarded as
compositions of several independent multipartite Bell experiments connected
together through a central node. For such networks we present tight Bell-type
inequalities which are satisfied by all classical correlations. We study
properties of the violations of our inequalities by probability distributions
arising in quantum theory.
