  Quantum networks are of high interest nowadays. In short, they describe the
distribution of quantum sources represented by edges to different parties
represented by nodes in the networks. Bundles of tools have been developed
recently to characterize quantum states from the network in the ideal case.
However, features of quantum networks in the noisy intermediate-scale quantum
(NISQ) era invalidate most of them and call for feasible tools. By utilizing
purity, covariance, and topology of quantum networks, we provide a systematic
approach to tackle with arbitrary quantum networks in the NISQ era, which can
be noisy, intermediate-scale, random, and sparse. One application of our method
is to witness the progress of essential elements in quantum networks, like the
quality of multipartite entangled sources and quantum memory.
