  A challenging problem in complex networks is the network reconstruction
problem from data. This work deals with a class of networks denoted as
conserved networks, in which a flow associated with every edge and the flows
are conserved at all non-source and non-sink nodes. We propose a novel
polynomial time algorithm to reconstruct conserved networks from flow data by
exploiting graph theoretic properties of conserved networks combined with
learning techniques. We prove that exact network reconstruction is possible for
arborescence networks. We also extend the methodology for reconstructing
networks from noisy data and explore the reconstruction performance on
arborescence networks with different structural characteristics.
