Learning Conserved Networks from Flows

The network reconstruction problem is one of the challenging problems in network science. This work deals with reconstructing networks in which the flows are conserved around the nodes. These networks are referred to as conserved networks. We propose a novel concept of conservation graph for describing conserved networks. The properties of conservation graph are investigated. We develop a methodology to reconstruct conserved networks from flows by combining these graph properties with learning techniques, with polynomial time complexity. We show that exact network reconstruction is possible for radial networks. Further, we extend the methodology for reconstructing networks from noisy data. We demonstrate the proposed methods on different types of radial networks.