Introduction
In this post I am showcasing some examples of using the Raku programming language to create and visualize graphs. These examples are part of a series of neat examples, which are concise or straightforward code snippets that produce compelling visual or textual outputs.
(And, hopefully, we know something is neat when we see it…)
All computational graph features discussed here are provided by the “Graph” module. The graphs are visualized using D3.js (via “JavaScript::D3”) and Graphviz DOT (via Graph.dot), providing both interactive and static visualizations.
Here is the link to the related presentation recording “Graph neat examples in Raku (Set 3):
Setup
The setup for these examples is the same as in the two sets, so it is skipped here.
Nested Graphs
Let us look first into nested graphs.
A nested graph is created by repeatedly applying a function to an initial value.
Here’s a basic example:
#% html my $g1 = Graph::Nested.new({$_ ** 2}, 2, 3, :directed); my $g2 = Graph::Nested.new({"f($_)"}, 'x', 3, :directed); $g1.dot(:$background, engine => 'dot', vertex-shape => 'ellipse', vertex-width => 0.75, :svg) ~ $g2.dot(:$background, engine => 'dot', vertex-shape => 'ellipse', vertex-width => 0.75, :svg) 
In this example, we start with a value and apply a function to it multiple times. The graph visually represents these nested applications.
Binary Tree
We can extend this concept by using two functions, creating a binary tree structure:
my $g = Graph::Nested.new({["f($_)", "g($_)"]}, 'x', 3, :directed) # Graph(vertexes => 15, edges => 14, directed => True) #%html $g.dot(node-width => 0.75, node-height => 0.3, node-shape => 'rect', engine => 'dot'):svg 
This creates a more complex graph where each node has two children, representing the application of two different functions.
Mod Graph
The mod graph example uses arithmetic operations to create a directed graph:
my $g = Graph::Nested.new({($_.Int ** 2 + 1) mod 10}, ^10, :directed) # Graph(vertexes => 10, edges => 10, directed => True) #%html $g.dot(node-width => 0.3, node-height => 0.3, node-shape => 'circle', engine => 'sfdp'):svg This graph shows how numbers transform through a series of operations, resulting in a directed cycle.
Range Graph
Finally, we have a range graph, which uses an integer range to create a graph:
my $g = Graph::Nested.new({^$_}, '9', 2, :directed) # Graph(vertexes => 10, edges => 45, directed => True) #%html $g.dot(node-width => 0.4, node-height => 0.4, node-font-size => 18, engine => 'dot', size => (6, 6)):svg 
This graph illustrates the concept of completeness and allows us to compute in-degrees and out-degrees of vertices.
$g.undirected-graph.is-complete # True say 'in : ', $g.vertex-in-degree(:pairs); say 'out : ', $g.vertex-out-degree():p; # in : (0 => 9 1 => 8 2 => 7 3 => 6 4 => 5 5 => 4 6 => 3 7 => 2 8 => 1 9 => 0) # out : (0 => 0 1 => 1 2 => 2 3 => 3 4 => 4 5 => 5 6 => 6 7 => 7 8 => 8 9 => 9) File System Graphs
RakuMode Notebooks
Next, let’s visualize file system structures as graphs. We’ll start by getting a list of file paths from a directory:
my @paths = paths($*HOME ~ "/MathFiles/RakuForPrediction"); my @paths2 = @paths>>.subst($*HOME.Str)>>.split("/", :skip-empty); @paths2.elems # 183 We then create graph edges from these paths:
my @edges = @paths2.map({ $_.rotor(2 => -1).map({ $_.head => $_.tail }) }).map(*.Slip).unique(:as({.Str})); my $g = Graph.new(@edges, :directed) # Graph(vertexes => 188, edges => 188, directed => True) And visualize the graph using Graphviz:
#%html my $preamble = q:to/END/; fontcolor = "Ivory"; fontsize = "12"; labelloc = "t"; label = "Directory paths"; graph [size="8,8!"]; bgcolor="none"; node [style=filled, fixedsize=true, shape=circle, color="Black", fillcolor="SlateBlue", penwidth=1, fontsize=4, fontcolor="Gray", labelloc=c, width=0.08, height=0.08]; edge [color="SteelBlue", penwidth=0.6, arrowsize=0.4]; END $g.dot(:$preamble, engine=>'twopi'):svg; 
Raku-doc Files
Finally, we’ll create a larger graph from the Raku documentation files:
my @paths = paths($*HOME ~ "/Downloads/doc/doc"); my @paths2 = @paths>>.subst($*HOME.Str)>>.split("/", :skip-empty); my @edges = @paths2.map({ $_.rotor(2 => -1).map({ $_.head => $_.tail }) }).map(*.Slip).unique(:as({.Str})); my $g2 = Graph.new(@edges, :directed) # Graph(vertexes => 476, edges => 510, directed => True) And plot it using D3.js:
#%js $g2.edges ==> js-d3-graph-plot( width => 1100, height => 400, :$background, :$title-color, vertex-size => 3, vertex-fill-color => 'SlateBlue', vertex-label-font-size => 10, vertex-label-color => 'none', edge-thickness => 1, directed => $g.directed, force => {charge => {strength => -50, iterations => 1}, y => {strength => 0.4}, collision => {radius => 2, iterations => 1}, link => {distance => 1}} ) 
Same graph, but with vertex names:
This visualization demonstrates the structure of the Raku documentation as a graph, offering insights into its organization.
Thank you for joining me in exploring these neat examples of graph visualization in Raku. I hope you will use Raku’s graph-functionalities a lot and often!
Raku for Prediction
One thought on “Graph Neat Examples in Raku – Set 3”