Function Repository Resource:

FoldGraph

Construct a graph by folding a list of arguments

Contributed by: Nikolay Murzin

ResourceFunction["FoldGraph"][f,{x₁,x₂,…},{y₁,y₂,…}]

constructs a graph with edges for each output of a multioutput function f applied to inputs x_i and iteratively to each y_i.

ResourceFunction["FoldGraph"][f,x,{y₁,y₂,…}]

is equivalent to ResourceFunction["FoldGraph"][f,{x},{y₁,y₂,…}].

ResourceFunction["FoldGraph"][f,{x,y₁,y₂,…}]

is equivalent to ResourceFunction["FoldGraph"][f,{x},{y₁,y₂,…}].

ResourceFunction["FoldGraph"][f]

represents an operator form of ResourceFunction["FoldGraph"] that can be applied to expressions.

Details and Options

Given that for each ith input at jth iteration the kth output of a function is denoted as o_{k, j}=f^k[o_{i, j-1},y_j] where f^kis the kth part of f. Initial outputs are the inputs o_{i, 0}=x_i, the resulting graph contains all edges connecting subsequent iterations o_i,j-1 o_{k, j}.

ResourceFunction["FoldGraph"][f,{}] produces an empty graph.

For every output of a function that has a Labeled head, take its first argument as a vertex and tag a corresponding edge with its second argument. The default head can be changed with the "TagHead" option of ResourceFunction["FoldGraph"].

ResourceFunction["FoldGraph"] supports all options of Graph.

Examples

Basic Examples (6)

Fold a single output function to make a graph:

In[1]:=

Out[1]=

Use the first element of the list as an initial vertex:

In[2]:=

Out[2]=

Fold with multiple inputs:

In[3]:=

Out[3]=

Fold a multi-output function:

In[4]:=

Out[4]=

Use arbitrary functions to define the vertices:

In[5]:=

Out[5]=

Tag edges:

In[6]:=

$ResourceFunction[ "FoldGraph"][{Labeled[#1 + #2, Row[{"+", #2}]], Labeled[#1 #2, Row[{"\[Times]", #2}]]} &, Range[4], VertexLabels -> Automatic, EdgeLabels -> "EdgeTag"]$