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EdgeWeight

is an option and annotation for Graph and related functions that specifies an edge weight.

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EdgeWeight

EdgeWeight

is an option and annotation for Graph and related functions that specifies an edge weight.

Details

  • The following option settings can be used:
  • Automaticautomatically determine edge weights
    {vivj->wij,…}edge has weight etc.
    {w1,w2,…}give all edge weights in the same order as used by EdgeList
    {patternw,…}edge that matches the pattern has weight w
  • The wrapper Annotation[vivj,EdgeWeight->w] can be used when creating graphs in functions such as Graph etc.
  • The weight can be any expression.
  • The weight can be interpreted as cost or capacity, or can have other special meanings for different graph computation functions.

Examples

Basic Examples  (3)

Set a weight for all edges:

Wolfram Language code: Graph[{12, 23, 31}, EdgeWeight -> {_ ? (OddQ[First[#]]&) -> -1}]

The weighted adjacency matrix:

Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

Specify the weight for individual edges:

Wolfram Language code: Graph[{12, 23, 31}, EdgeWeight -> {12 -> 2}]

The list of edge weights in the order given in the graph:

Wolfram Language code: AnnotationValue[%, EdgeWeight]

Use any expression as a weight:

Wolfram Language code: CompleteGraph[4, EdgeWeight -> {a, b, c, d, e, f}]
Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm
Wolfram Research (2010), EdgeWeight, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeWeight.html (updated 2020).

Text

Wolfram Research (2010), EdgeWeight, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeWeight.html (updated 2020).

CMS

Wolfram Language. 2010. "EdgeWeight." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/EdgeWeight.html.

APA

Wolfram Language. (2010). EdgeWeight. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EdgeWeight.html

BibTeX

@misc{reference.wolfram_2026_edgeweight, author="Wolfram Research", title="{EdgeWeight}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeWeight.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_edgeweight, organization={Wolfram Research}, title={EdgeWeight}, year={2020}, url={https://reference.wolfram.com/language/ref/EdgeWeight.html}, note=[Accessed: 13-June-2026]}