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 Tree

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Cite this as:

Weisstein, Eric W. "Weighted Graph." From MathWorld--A Wolfram Web Resource.

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