Which are the standard graph properties?

Question

Graph objects can have different kinds of "properties":

• vertex properties
• edge properties
• graph properties

Each of these can be standard ones, such as EdgeWeight, which are stored as options taking the values of a list. Or they can be custom properties, which are stored in the Properties option.

Example:

g = Graph[{1 <-> 2, 2 <-> 3}];

In[]:= SetProperty[{g, 1}, "shoo" -> 3] // InputForm
Out[]= Graph[{1, 2, 3}, {UndirectedEdge[1, 2], UndirectedEdge[2, 3]}, 
 {Properties -> {1 -> {"shoo" -> 3}}}]

In[]:= SetProperty[{g, 1}, VertexCapacity -> 3] // InputForm
Out[]= Graph[{1, 2, 3}, {UndirectedEdge[1, 2], UndirectedEdge[2, 3]}, 
 {VertexCapacity -> {3, 1, 1}}]

Notice that a custom property can be set for a single vertex only while a standard property is set for all vertices and takes a default value for vertices which were not specified.

I am looking for a full list of standard graph properties along with their default values (when there is one).

I need this to implement robust and easy to use property remapping.

Answer 1

Property name        Refers to       Stored as        Default
-------------------------------------------------------------

VertexWeight         vertices        list             1
VertexCapacity       vertices        list             1
VertexCoordinates    vertices        list             none (*)

VertexSize           vertices        rules
VertexShape          vertices        rules
VertexShapeFunction  vertices        rules
VertexStyle          vertices        rules
VertexLabels         vertices        rules
VertexLabelStyle     vertices        rules

EdgeWeight           edges           list             1
EdgeCapacity         edges           list             1
EdgeCost             edges           list             1

EdgeStyle            edges           rules
EdgeShapeFunction    edges           rules
EdgeLabels           edges           rules
EdgeLabelStyle       edges           rules

^{* VertexCoordinates is special in that it can only be set for an individual vertex if all vertices have already been assigned an explicit coordinate value using SetProperty[graph, VertexCoordinates -> {...}]. It has no default.}

A vertex property can be set for individual vertices as SetProperty[{g, vertex}, prop -> value]. Similarly, an edge property can be set for individual edges as SetProperty[{g, edge}, prop -> value]. A graph property can only be set as SetProperty[g, prop -> value] for the complete graph.

List type properties are stored as a list of the same length as the number of elements they refer to (edges or vertices). When setting a list type property for in individual element (vertex or edge), the rest automatically get a default value. When setting a list type property for the whole graph, the length of the list must agree with the number of elements. Example:

SetProperty[g, VertexCapacity -> {1,2,3}] (* list length *must* agree with VertexCount *)

Rule type properties as stored as a list of rules, and may be assigned for a subset of elements (leaving the rest without an explicit value). Example:

g = Graph[{a,b,c}, ...];
SetProperty[g, VertexSize -> {a -> 1, b -> 2}] (* c will not have an assigned VertexSize *)

Rule type properties can also have a default value stored as the first element of the rule list. For certain types of properties (e.g. EdgeStyle), this default will be combined with the individual values. Example:

g = Graph[{1 <-> 2, 2 <-> 3}];    
SetProperty[g, EdgeStyle -> {Thick, 2 \[UndirectedEdge] 3 -> Red}]

Thick will apply to all edges, including 2 <-> 3, while Red will apply only to 2 <-> 3.