Conserved networks are a class of complex networks arising in several fields ranging from power to biological networks. In these networks, the flow attributes (such as energy, current, mass, flow rate, flux, etc.) are conserved at the nodes and hence, they are referred to as conserved networks. Information of network topology is essential for analysis and control of conserved networks. This work deals with identifying the topology of conserved networks from data, an important problem in network science. In this work, we show that given the flows captured at steady-state, the underlying graph of conserved networks can be learnt by exploiting the conservation laws. In this seminar, network topology identification for two types of networks: (i) networks having arborescence structure (arborescence networks) and (ii) networks having non-arborescence structure, will be discussed. The proposed methodologies elegantly combine a machine learning technique of Principal Component Analysis (PCA) with graph-theoretic concepts to identify the desired graph from data. Firstly, it is shown that f-cutset matrices corresponding to all spanning trees of the graph can be determined from flow data using PCA. Using this result, a methodology is developed to exactly identify the underlying arborescence network. For networks with non-arborescence structure, it is shown that knowing the connectivity of one of the spanning trees of the graph is a sufficient condition for exact identification of the underlying network. These methodologies can be extended to even noisy data by using different variants of PCA. The algorithms developed for learning topology based on theory and methodologies established, are of polynomial time complexity. Simulation studies are performed on randomly generated networks to corroborate that the methods run in polynomial time and are robust to even noisy measurements.