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Network topology refers to the structure of a network represented as a graph with edges connected between a set of nodes. This topology information is essential for monitoring, analysis, optimization, and control of networks. In practice, at times, network topology may be unknown, only partially known or incorrectly reported. To address these issues, this work aims to solve three related problems with respect to topology of a class of networks known as conserved networks, from flow data: (i) topology identification - identifying the complete topology, (ii) topology completion - inferring unknown edges when the topology is partially known, and (iii) topology verification - verifying if there are any errors in the reported topology. The results and methodologies to address these problems are developed using multivariate data analysis, graph theory, and control theory. The algorithms developed based on the proposed methodologies are shown to be of polynomial time complexity. The theoretical findings are corroborated through simulations.