Graph annotations¶

A graph carries its annotations as options of its own, which Options reads back:

$ wo 'Options[Graph[{1 <-> 2, 2 <-> 3}, EdgeWeight -> {5, 7}]]'
{EdgeWeight -> {5, 7}}

AnnotationValue and PropertyValue name one vertex or edge to read the value it carries; a property the graph does not have gives $Failed:

$ wo 'PropertyValue[{Graph[{1 <-> 2, 2 <-> 3}, EdgeWeight -> {5, 7}], 2 <-> 3}, EdgeWeight]'
7

$ wo 'AnnotationValue[{Graph[{1 <-> 2}, EdgeWeight -> {5}], 1}, VertexWeight]'
$Failed

An item named by a rule reads back the bare value the rule gives it:

$ wo 'AnnotationValue[{Graph[{1 -> 2, 2 -> 3}, VertexLabels -> {1 -> "a"}], 1}, VertexLabels]'
a

AnnotationKeys lists the annotations a graph, or one of its vertices or edges, offers:

$ wo 'AnnotationKeys[{Graph[{1 -> 2, 2 -> 3}], 1}]'
{VertexCoordinates, VertexShapeFunction, VertexShape, VertexSize, VertexStyle}

AnnotationDelete drops a whole annotation, or just one item's share of it — a weight spelled out per item falls back to 1 rather than losing the key:

$ wo 'Options[AnnotationDelete[Graph[{1 <-> 2}, EdgeWeight -> {5}], EdgeWeight]]'
{}

$ wo 'Options[AnnotationDelete[{Graph[{1 <-> 2, 2 <-> 3}, EdgeWeight -> {5, 7}], 1 <-> 2}, EdgeWeight]]'
{EdgeWeight -> {1, 7}}

SetProperty writes one:

$ wo 'Options[SetProperty[{Graph[{1 <-> 2}], 1 <-> 2}, EdgeWeight -> 7]]'
{EdgeWeight -> {7}}

The weight predicates say what kind of weights a graph carries:

$ wo 'EdgeWeightedGraphQ[Graph[{1 <-> 2}, EdgeWeight -> {5}]]'
True

$ wo 'VertexWeightedGraphQ[Graph[{1 <-> 2}, EdgeWeight -> {5}]]'
False

In an EdgeTaggedGraph every edge carries a tag; one written without a tag is tagged by how many copies of it came before:

$ wo 'ToString[EdgeList[EdgeTaggedGraph[{1 <-> 2, 2 <-> 3}]], InputForm]'
{UndirectedEdge[1, 2, 1], UndirectedEdge[2, 3, 1]}

$ wo 'EdgeTags[EdgeTaggedGraph[{UndirectedEdge[1, 2, "a"], 2 <-> 3}]]'
{a, 1}