VertexWeight

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

Details

The following option settings can be used:
{w₁,w₂,…} give all vertex weights in the same order as used by VertexList
The wrapper Annotation[v,VertexWeight->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 have other special meanings for different graph computation functions.

Examples

Set the weight for all vertices:

Wolfram Language code: Graph[{12, 23, 31}, VertexWeight -> {2, 3, 4}]

Wolfram Language code: AnnotationValue[{%, 1}, VertexWeight]

Use any expression as a weight:

Wolfram Language code: Graph[{12, 23, 31}, VertexWeight -> {[image], [image], "Sin[x]"}]

Wolfram Language code: AnnotationValue[{%, 1}, VertexWeight]

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