#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11109069 # clique
use warnings;
use List::Util qw( uniq );

my $edges = <<END; # from https://en.wikipedia.org/wiki/Clique_(graph_theory)
[1,2],[1,3],[1,4],
[2,3],[2,4],
[3,4],
[4,5],[23,4],
[5,6],[5,7],[5,8],
[6,7],
[7,8],
[8,9],[10,8],
[10,9],[11,9],[12,9],[13,9],
[10,13],
[11,12],[11,13],
[12,13],
[13,14],
[14,15],[14,21],
[15,16],[15,17],[15,19],
[16,17],
[17,18],[17,19],
[18,19],[18,20],[18,21],
[19,20],[19,21],[19,22],
[20,23],
[21,22],[21,23],
[22,23],
END

$edges =~ s/(?<=\[)[\w,]+(?=\])/ join ',', sort split ',', $& /ge;  # fix order
print "$edges\n";
my %edges = map +( $_ => '(*FAIL)' ), $edges =~ /\w+,\w+/g;
my %cliques;
my %seen;

find( uniq sort $edges =~ /\w+/g );                     # start with every node

sub find
  {
  $seen{ my $set = "@_" }++ and return;
  if( my @out = $set =~ /\b(\w+)\b.+\b(\w+)\b(??{ $edges{"$1,$2"} || "" })/ )
    {
    for my $node ( @out )     # pair of unconnected nodes, try without each one
      {
      @_ > 3 and find( grep $_ ne $node, @_ );
      }
    }
  else
    {
    $cliques{ $set }++;                                 # it is fully connected
    }
  }

my $uniquecliques = '';
for ( sort { length $b <=> length $a } sort +uniq
  keys %cliques, map tr/,/ /r, keys %edges )
  {
  my $pattern =  " $_ " =~ s/\w+/\\b$&\\b/gr =~ s/ /.*?/gr;
  $uniquecliques =~ /^$pattern$/m or $uniquecliques .= "$_\n";
  }

print $uniquecliques;

##</code><code>##

[1,2],[1,3],[1,4],
[2,3],[2,4],
[3,4],
[4,5],[23,4],
[5,6],[5,7],[5,8],
[6,7],
[7,8],
[8,9],[10,8],
[10,9],[11,9],[12,9],[13,9],
[10,13],
[11,12],[11,13],
[12,13],
[13,14],
[14,15],[14,21],
[15,16],[15,17],[15,19],
[16,17],
[17,18],[17,19],
[18,19],[18,20],[18,21],
[19,20],[19,21],[19,22],
[20,23],
[21,22],[21,23],
[22,23],

11 12 13 9
15 16 17
15 17 19
17 18 19
18 19 20
18 19 21
19 21 22
21 22 23
1 2 3 4
10 13 9
10 8 9
13 14
14 15
14 21
20 23
5 6 7
5 7 8
23 4
4 5