NestGraphTagged

A version of NestGraph in which edges corresponding to different outputs are tagged differently

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

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

Details and Options

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 function f[expr] returns values of the form expr→tag, then those tags are used instead. This can be modified with "TagHead" option.

NestGraph takes the same options as Graph.

ResourceFunction["NestGraphTagged"] accepts the following options:

"StateLabeling"

False

whether to render states as boxes

"RuleStyling"

Automatic

list of styles for edges/rules

"FormattingFunction"

Automatic

how to format state

"PostProcessGraph"

Identity

post process graph

"TagHead"

Rule

custom head to associate tags with output values

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:

In[1]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1}, 1, 4]$

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Use pure function:

In[2]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][{# - 1, 2 #} &, 1, 4]$

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Use a list of initial expressions:

In[3]:=

$f[n_] := {n + 1, 2 n, 3 n - 1} ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][f, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 4]$

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Add a legend to explain colors:

In[5]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1, n - 1}, {1}, 4, PlotLegends -> TraditionalForm /@ {2 n, n + 1, n - 1}]$

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Label the vertex states in a nested graph:

In[6]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][{2 #, # + 1} &, {1}, 4, "StateLabeling" -> True]$

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Scope (4)

Edge colorings can be overridden:

In[7]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1}, {1}, 4, "RuleStyling" -> {Black, Orange}]$

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Add labels to edges:

In[8]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1}, {1}, 4, EdgeLabels -> { DirectedEdge[_, _, t_] /; OddQ[t] :> Placed[t, {1/2, {-1, 1/2}}], DirectedEdge[_, _, t_] /; EvenQ[t] :> Placed[t, {1/2, {1, 1/2}}]}, EdgeLabelStyle -> Directive[12, Bold]]$

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Add tooltips to edges:

In[9]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1}, {1}, 4, EdgeLabels -> Placed["EdgeTag", Tooltip]]$

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An alternate type of edge labeling:

In[10]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {n + 2, n + 3}, 0, 4, "StateLabeling" -> True, EdgeLabels -> { 1 -> Placed["+2", {.7, {-.2, 0}}], 2 -> Placed["+3", {.7, {-.2, 0}}] }]$

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Make custom edge tags by constructing rule values:

In[11]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][ s |-> # -> # & /@ StringReplaceList[s, {"A" -> "AB", "B" -> "A"}], "A", 3, "StateLabeling" -> True, EdgeLabels -> "EdgeTag"]$

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Options (5)

StateLabeling (1)

Turn on special vertex shapes:

In[12]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][{2 #, # + 1} &, {1}, 4, "StateLabeling" -> True]$

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FormattingFunction (1)

Change the formatting for vertex 31:

In[13]:=

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

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RuleStyling (1)

Use custom styles for output values:

In[14]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1}, {1}, 4, "RuleStyling" -> {Black, Orange}]$

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PostProcessGraph (1)

If the output is graphics, it useful to apply some custom function to the graph itself:

In[15]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][n |-> {2 n, n + 1, n - 1}, {1}, 4, "PostProcessGraph" -> ReverseGraph, PlotLegends -> TraditionalForm /@ {2 n, n + 1, n - 1}]$

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TagHead (1)

Instead of Rule, use custom head to specify edge tags:

In[16]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][ s |-> Labeled[#, #] & /@ StringReplaceList[s, {"A" -> "AB", "B" -> "A"}], "A", 3, "StateLabeling" -> True, EdgeLabels -> "EdgeTag", "TagHead" -> Labeled]$

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Neat Examples (2)

Vertices can be number pairs:

In[17]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][ v |-> {{{1, 0}, {1, 1}} . v, {{1, 1}, {0, 0}} . v}, {{1, 1}}, 3, "StateLabeling" -> True]$

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For a remainder graph, to find 2143 (mod 7), start at 0 and follow (2143) to get remainder 1:

In[18]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/nikm/DeployedResources/Function/\ NestGraphTagged"][v |-> Mod[{v + 1, 10 v}, 7], Range[1], 10, "StateLabeling" -> True, GraphLayout -> "CircularEmbedding"]$

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