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of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). This distance function, while well defined, is not a metric. There need be no restrictions on the weights other than the need to be able to combine and compare them, so negative weights are used in some applications. Since paths are directed, symmetry can not be guaranteed, and if negative-weight cycles exist the distance matrix may not be hollow (and in the absence of a bound on the step count,

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