Function Repository Resource:

NestGraphTagged

Source Notebook

Create a graph by successively applying a function and differently tagging edges corresponding to different outputs

Contributed by: Nikolay Murzin and Ed Pegg Jr.

ResourceFunction["NestGraphTagged"][f,expr,n]

gives the tagged graph obtained by starting with expr and applying f successively n times.

Details and Options

The expr can be any expression.

ResourceFunction["NestGraphTagged"][f,expr] is equivalent to ResourceFunction["NestGraphTagged"][f,expr,1].

ResourceFunction["NestGraphTagged"][f,expr] gives a graph with tagged edges

, where f[expr] evaluates to {expr₁,…,expr_k}.

If a function f[expr] returns a list values of the form tag→expr or an association <|tag₁→expr₁,tag₂→expr₂,…|>, then those tags are used instead.

ResourceFunction["NestGraphTagged"] takes the same options as Graph with the following additions:

"StateLabeling"

False

whether to render states as boxes

"RuleStyling"

Automatic

list of styles for edges/rules

"FormattingFunction"

Automatic

how to format a state

"PostProcessGraph"

Identity

post-process graph

Any None on the right-hand side of the rule is dropped from the graph.

One can use integers in place of tagged directed edges to specify EdgeLabels.

PlotLegends can be used to get a legend for different edge rules.

Examples

Basic Examples (5)

Make a nested graph with edge coloring:

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Use a pure function:

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Use a list of initial expressions:

In[3]:=

$f[n_] := {n + 1, 2 n, 3 n - 1} ResourceFunction[ "NestGraphTagged"][f, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 4]$

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Add a legend to explain colors:

In[5]:=

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Label the vertex states in a nested graph:

In[6]:=

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Scope (6)

Edge colorings can be overridden:

In[7]:=

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Add labels to edges with EdgeLabels and a pattern:

In[8]:=

$ResourceFunction["NestGraphTagged"][n |-> {2 n, n + 1}, {1}, 4, EdgeLabels -> { DirectedEdge[_, _, t_] /; OddQ[t] :> Placed[t, {1/2, {-1, 1/2}}], DirectedEdge[_, _, t_] /; EvenQ[t] :> Placed[t, {1/2, {1, 1/2}}]}, EdgeLabelStyle -> Directive[12, Bold]]$

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Add edge labels using output index:

In[9]:=

ResourceFunction["NestGraphTagged"][n |-> {n + 2, n + 3}, 0, 4, "StateLabeling" -> True, EdgeLabels -> {
1 -> Placed["+2", {.7, {-.2, 0}}], 2 -> Placed["+3", {.7, {-.2, 0}}]
}]

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Add tooltips to edges:

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Make custom edge tags by returning a list of rules (tags will be pairs of the form {key, index}):

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Make custom edge tags by returning an association:

In[12]:=

$ResourceFunction["NestGraphTagged"][ n |-> <|"\[Times]2" -> 2 n, "+1" -> n + 1|>, 2, 3, "StateLabeling" -> True, EdgeLabels -> "EdgeTag"]$

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Options (4)

StateLabeling (1)

Turn on special vertex shapes:

In[13]:=

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FormattingFunction (1)

Change the formatting for vertex 31:

In[14]:=

$ResourceFunction["NestGraphTagged"][ n |-> Mod[{2 n + 1, 3 n + 1}, 144], {1}, 200, "StateLabeling" -> True, "FormattingFunction" -> (# /. {31 -> Style[31, Red, Bold, 16], x_ :> Style[x, Black]} &)]$