  The quantum network correlations play significant roles in long distance
quantum communication,quantum cryptography and distributed quantum computing.
Generally it is very difficult to characterize the multipartite quantum network
correlations such as nonlocality, entanglement and steering. In this paper, we
propose the network and the genuine network quantum steering models from the
aspect of probabilities in the star network configurations. Linear and
nonlinear inequalities are derived to detect the network and genuine network
quantum steering when the central party performs one fixed measurement. We show
that our criteria can detect more quantum network steering than that from the
violation of the n-locality quantum networks. Moreover, it is shown that
biseparable assemblages can demonstrate genuine network steering in the star
network configurations.
