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A critical review of the literature of shortest paths in networks that examines methods for determining (1) the shortest path between two specified nodes; (2) the shortest path between all pairs of nodes; (3) the second, third, etc., shortest path; (4) the fastest path through a network with travel times depending on the departure time; and (5) the shortest path between specified endpoints that passes through specified intermediate nodes. Inefficient algorithms, erroneous procedures, and false assumptions in the current literature are identified.