Weighted Graph
A weighted graph is a graph in which vertices, edges, or both vertices and edges are assigned numerical values known as weights. A weighted graph is therefore a special type of labeled graph in which the labels are numbers (most commonly taken as nonnegative or positive).
A graph containing a weight for each vertex is known as a vertex-weighted graph, while a graph with a weight for each edge is known as an edge-weighted graph.
See also
Labeled Graph, Taylor's Condition, Weighted TreeExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Weighted Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WeightedGraph.html