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Recently, several algorithms for deciding whether all origin-destination (O-D) flows are reconstructable based on the measurement of a subset of link flows have been proposed in the literature. The algorithms discussed in this paper have been introduced as ??algebraic?? and ??topological?? approaches by their corresponding authors. However, a detailed discussion on the properties of the results delivered by the considered algorithms, including statistical properties of the corresponding estimated O-D flows, is still lacking. This paper closes this gap by providing an interpretation of the algorithms demonstrating their potential when jointly applied and elucidating the properties of the results provided by the algorithms.