## AbstractWe encountered special types of paths when dealing with transport problems in graphs and networks. A path defined by its successive vertices u1,u2,…,ul is called concave if for any vertex x of a graph (or a network) the sequence of distances D (x,u1 ),D (x,u2 ),…,D(x,ul ) is at first monotonically increasing and then monotonically decreasing. The paper presents some properties of concave paths and an algorithm for finding concave paths of maximal length.
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