An edge length is a nonnegative numerical label assigned to an edge of a graph to measure the length or cost of traversing it. A path's length is the sum of its edge lengths, and the shortest-path distance is the infimum of these sums. This metric use is more restrictive than a general edge weight, which can be negative in other models.
For a triangle with edge lengths , , and , the shortest distance from to is five via , although the direct edge has length ten. Thus edge length and vertex-to-vertex distance need not coincide.
Strictly positive lengths on a finite connected graph give a metric on its vertices. Zero-length edges can identify distinct vertices at distance zero, producing a pseudometric; negative edges can destroy the metric interpretation. The labels need not equal the apparent lengths of edges in a drawing.
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