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Some improvements and additions to the SimpleGraph.pl macro. #1379

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Some improvements and additions to the SimpleGraph.pl macro. #1379

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8b9d93a
Change the weight color used from red to FireBrick.
drgrice1 Feb 4, 2026
87f4a0b
Add a `components` method that returns the components of the graph.
drgrice1 Mar 3, 2026
2abaee7
Improve label positioning.
drgrice1 Mar 4, 2026
da670d0
Fix a bug in the `edgeSet` method that results in the method returning
drgrice1 Mar 4, 2026
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117 changes: 76 additions & 41 deletions macros/math/SimpleGraph.pl
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Original file line number Diff line number Diff line change
Expand Up @@ -135,7 +135,7 @@ sub randomGraphWithoutEulerTrail {
my $graph;

do {
$graph = simpleGraphWithDegreeSequence([ map { main::random(2, $size - 1, 1) } 0 .. $size - 1 ], %options);
$graph = simpleGraphWithDegreeSequence([ map { main::random(2, $size - 1) } 0 .. $size - 1 ], %options);
} while !defined $graph || $graph->hasEulerTrail;

return $graph->setRandomWeights(
Expand Down Expand Up @@ -543,7 +543,7 @@ sub edgeSet {
}
}

my $edgeSet = GraphTheory::SimpleGraph::Value::EdgeSet->new($context, @edgeSet);
my $edgeSet = GraphTheory::SimpleGraph::Value::EdgeSet->new($context, \@edgeSet);
$edgeSet->{open} = '{';
$edgeSet->{close} = '}';
return $edgeSet;
Expand Down Expand Up @@ -645,6 +645,37 @@ sub numComponents {
return $result;
}

sub components {
my $self = shift;

my @adjacencyMatrix = map { [@$_] } @{ $self->{adjacencyMatrix} };

for my $i (0 .. $#adjacencyMatrix) {
for my $j ($i + 1 .. $#adjacencyMatrix) {
if ($adjacencyMatrix[$i][$j] != 0) {
for my $k (0 .. $#adjacencyMatrix) {
$adjacencyMatrix[$j][$k] += $adjacencyMatrix[$i][$k];
$adjacencyMatrix[$k][$j] += $adjacencyMatrix[$k][$i];
}
}
}
}

my @components;
for my $i (reverse(0 .. $#adjacencyMatrix)) {
my $componentFound = 0;
for (@components) {
next unless $adjacencyMatrix[ $_->[-1] ][$i];
$componentFound = 1;
unshift(@$_, $i);
last;
}
push(@components, [$i]) unless $componentFound;
}

return main::PGsort(sub { $_[0][0] < $_[1][0] }, @components);
}

sub edgeWeight {
my ($self, $i, $j, $weight) = @_;
if (defined $weight) {
Expand Down Expand Up @@ -796,11 +827,10 @@ sub image {
$plot->add_point(@$iVertex, color => 'blue', mark_size => 3);

$plot->add_label(
1.25 * $iVertex->[0], 1.25 * $iVertex->[1],
label => "\\\\($self->{labels}[$i]\\\\)",
$iVertex->[0], $iVertex->[1], "\\\\($self->{labels}[$i]\\\\)",
color => 'blue',
h_align => 'center',
v_align => 'middle'
anchor => 180 + $i * $gap * 180 / $main::PI,
padding => 8
) if $graphOptions{showLabels};

my $u = 0.275;
Expand All @@ -818,8 +848,8 @@ sub image {
$plot->add_label(
$u * $iVertex->[0] + $v * $jVertex->[0] + $perp[0] * 0.06,
$u * $iVertex->[1] + $v * $jVertex->[1] + $perp[1] * 0.06,
label => "\\\\($self->{adjacencyMatrix}->[$i][$j]\\\\)",
color => 'red',
"\\\\($self->{adjacencyMatrix}->[$i][$j]\\\\)",
color => 'FireBrick',
rotate => ($perp[0] < 0 ? 1 : -1) *
atan2(sqrt(1 - $perp[1] * $perp[1]), $perp[1]) * 180 /
$main::PI - ($perp[1] < 0 ? 180 : 0)
Expand Down Expand Up @@ -867,11 +897,10 @@ sub gridLayoutImage {
my $y = $gridGap * ($self->{gridLayout}[0] - $i - 1);
$plot->add_point($x, $y, color => 'blue', mark_size => 3);
$plot->add_label(
$x - $labelShift, $y + 2 * $labelShift,
label => "\\\\($self->{labels}[$i + $self->{gridLayout}[0] * $j]\\\\)",
$x, $y, "\\\\($self->{labels}[$i + $self->{gridLayout}[0] * $j]\\\\)",
color => 'blue',
h_align => 'center',
v_align => 'middle'
anchor => -atan2(2, 1) * 180 / $main::PI,
padding => 8,
) if $graphOptions{showLabels};
}
}
Expand All @@ -891,14 +920,14 @@ sub gridLayoutImage {
($self->{gridLayout}[0] - ($j % $self->{gridLayout}[0]) - 1) * $gridGap
];
$plot->add_dataset($iVertex, $jVertex, color => 'black', width => 1);
my $vector = [ $jVertex->[0] - $iVertex->[0], $jVertex->[1] - $iVertex->[1] ];
if ($graphOptions{showWeights}) {
my $norm = sqrt($vector->[0]**2 + $vector->[1]**2);
my $vector = [ $jVertex->[0] - $iVertex->[0], $jVertex->[1] - $iVertex->[1] ];
$plot->add_label(
$u * $iVertex->[0] + $v * $jVertex->[0] - $vector->[1] / $norm * 2,
$u * $iVertex->[1] + $v * $jVertex->[1] + $vector->[0] / $norm * 2,
label => "\\\\($self->{adjacencyMatrix}[$i][$j]\\\\)",
color => 'red'
$u * $iVertex->[0] + $v * $jVertex->[0],
$u * $iVertex->[1] + $v * $jVertex->[1],
"\\\\($self->{adjacencyMatrix}[$i][$j]\\\\)",
color => 'FireBrick',
anchor => atan2(-$vector->[0], $vector->[1]) * 180 / $main::PI
);
}
}
Expand Down Expand Up @@ -969,21 +998,21 @@ sub bipartiteLayoutImage {
for my $i (0 .. $#$top) {
$plot->add_point($i * $width + $shift[0], $high, color => 'blue', mark_size => 3);
$plot->add_label(
$i * $width + $shift[0], $high + 2 / 3,
label => "\\\\($self->{labels}[$top->[$i]]\\\\)",
$i * $width + $shift[0], $high, "\\\\($self->{labels}[$top->[$i]]\\\\)",
color => 'blue',
h_align => 'center',
v_align => 'bottom'
v_align => 'bottom',
padding => 8
) if $graphOptions{showLabels};
}
for my $j (0 .. $#$bottom) {
$plot->add_point($j * $width + $shift[1], $low, color => 'blue', mark_size => 3);
$plot->add_label(
$j * $width + $shift[1], $low - 2 / 3,
label => "\\\\($self->{labels}[$bottom->[$j]]\\\\)",
$j * $width + $shift[1], $low, "\\\\($self->{labels}[$bottom->[$j]]\\\\)",
color => 'blue',
h_align => 'center',
v_align => 'top'
v_align => 'top',
padding => 8
) if $graphOptions{showLabels};
}

Expand All @@ -997,12 +1026,13 @@ sub bipartiteLayoutImage {
$plot->add_dataset($point1, $point2, color => 'black');
if ($graphOptions{showWeights}) {
my $vector = [ $point2->[0] - $point1->[0], $point2->[1] - $point1->[1] ];
my $norm = sqrt($vector->[0]**2 + $vector->[1]**2);
$plot->add_label(
$u * $point1->[0] + $v * $point2->[0] - $vector->[1] / $norm * 5 / 4,
$u * $point1->[1] + $v * $point2->[1] + $vector->[0] / $norm * 5 / 4,
label => "\\\\($self->{adjacencyMatrix}[ $top->[$i] ][ $bottom->[$j] ]\\\\)",
color => 'red'
$u * $point1->[0] + $v * $point2->[0],
$u * $point1->[1] + $v * $point2->[1],
"\\\\($self->{adjacencyMatrix}[ $top->[$i] ][ $bottom->[$j] ]\\\\)",
color => 'FireBrick',
anchor => atan2($vector->[0], -$vector->[1]) * 180 / $main::PI + 180,
padding => 2
);
}
}
Expand Down Expand Up @@ -1039,11 +1069,10 @@ sub wheelLayoutImage {

$plot->add_point(0, 0, color => 'blue', mark_size => 3);
$plot->add_label(
0.1, 0.2,
label => "\\\\($self->{labels}[ $self->{wheelLayout} ]\\\\)",
0, 0, "\\\\($self->{labels}[ $self->{wheelLayout} ]\\\\)",
color => 'blue',
h_align => 'center',
v_align => 'middle'
anchor => 180 + $gap * 90 / $main::PI,
padding => 10
) if $graphOptions{showLabels};

for my $i (0 .. $self->lastVertexIndex) {
Expand All @@ -1055,11 +1084,10 @@ sub wheelLayoutImage {
$plot->add_point(@$iVertex, color => 'blue', mark_size => 3);

$plot->add_label(
1.25 * $iVertex->[0], 1.25 * $iVertex->[1],
label => "\\\\($self->{labels}[$i]\\\\)",
$iVertex->[0], $iVertex->[1], "\\\\($self->{labels}[$i]\\\\)",
color => 'blue',
h_align => 'center',
v_align => 'middle'
anchor => 180 + $iRel * $gap * 180 / $main::PI,
padding => 8
) if $graphOptions{showLabels};

if ($self->hasEdge($self->{wheelLayout}, $i)) {
Expand All @@ -1070,8 +1098,8 @@ sub wheelLayoutImage {
$plot->add_label(
0.5 * $iVertex->[0] + $iVertex->[1] / $norm * 0.1,
0.5 * $iVertex->[1] - $iVertex->[0] / $norm * 0.1,
label => "\\\\($self->{adjacencyMatrix}->[ $self->{wheelLayout} ][$i]\\\\)",
color => 'red',
"\\\\($self->{adjacencyMatrix}->[ $self->{wheelLayout} ][$i]\\\\)",
color => 'FireBrick',
rotate => ($perp[0] < 0 ? 1 : -1) *
atan2(sqrt(1 - $perp[1] * $perp[1]), $perp[1]) * 180 /
$main::PI - ($perp[1] < 0 ? 180 : 0)
Expand All @@ -1095,8 +1123,8 @@ sub wheelLayoutImage {
$plot->add_label(
0.5 * $iVertex->[0] + 0.5 * $jVertex->[0] + $vector[1] / $norm * 0.1,
0.5 * $iVertex->[1] + 0.5 * $jVertex->[1] - $vector[0] / $norm * 0.1,
label => "\\\\($self->{adjacencyMatrix}->[$i][$j]\\\\)",
color => 'red',
"\\\\($self->{adjacencyMatrix}->[$i][$j]\\\\)",
color => 'FireBrick',
rotate => ($perp[0] < 0 ? 1 : -1) *
atan2(sqrt(1 - $perp[1] * $perp[1]), $perp[1]) * 180 /
$main::PI - ($perp[1] < 0 ? 180 : 0)
Expand Down Expand Up @@ -2242,6 +2270,13 @@ =head2 numComponents

This method returns the number of connected components in the graph.

=head2 components

@c = $graph->components;

This method returns an array containing references to arrays that form a
partition of the vertex indices into the connected components of the graph.

=head2 edgeWeight

$c = $graph->edgeWeight($i, $j);
Expand Down