A graph metric is the shortest-path metric on the vertex set of a finite connected graph whose edges have strictly positive lengths. The distance between two vertices is the minimum sum of the lengths of the edges along a connecting path. Assigning weight 1 to every graph edge gives the usual graph distance.
Graph Metric
See also
Graph Distance, Metric Embedding Distortion, Planar Graph, Weighted GraphExplore with Wolfram|Alpha
References
Lück, W. "Survey on Geometric Group Theory." Münster J. Math. 1, 73-108, 2008. https://arxiv.org/abs/0806.3771.Cite this as:
Weisstein, Eric W. "Graph Metric." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphMetric.html