(not really trivial)

use warnings;
use strict;

use Data::Dump;

my @AoA = (
    [11,29, 10,25],
    [15,35, 11,29],
    [15,15, 11,21],
    [10,25, 11,21],
    [15,35, 21,39],
    [25,40, 21,39],
    [21,11, 25,10],
    [15,15, 21,11],
    [35,35, 29,39],
    [29,39, 25,40],
    [35,15, 29,11],
    [25,10, 29,11],
    [40,25, 39,29],
    [35,35, 39,29],
    [39,21, 40,25],
    [35,15, 39,21],
   );

$"=",";
my %neighbor;

for ( @AoA) {
    my ($a,$b)= ("@$_[0,1]", "@$_[2,3]") ;
    push @{$neighbor{$b}}, $a;
    push @{$neighbor{$a}}, $b;
  };



#dd \%neighbor;


#---  init
my $next;
my @path;
my ($last,$current)=("11,29","10,25");   # start
push @path, $last, $current;
delete $neighbor{$last};

while ( %neighbor) { 
  my $a_neighbors = delete $neighbor{$current};
  die "Data corrupt: $current has no more neighbors" unless $a_neighbo
+rs;
  ($next) = grep { $_ ne $last } @$a_neighbors;
  ($last,$current)=($current,$next);
  push @path, $current ;
}
  

#dd \@path;

my @flat= map { split ",", $_ } @path;   

print join ",", @flat;
[download]

output

11,29,10,25,11,21,15,15,21,11,25,10,29,11,35,15,39,21,40,25,39,29,35,3
+5,29,39,25,40,21,39,15,35,11,29
[download]

Thanks Rolf, that is very similar to the approach I was attempting myself. Unfortunately it only works when the line segments represent a complete cycle - see my comment below.

> Unfortunately it only works when the line segments represent a complete cycle

Nope!

You just have to handle the case that $next becomes undef and leave the loop.

The problem I rather see is to choose a starting point!

Simplest solution: you choose one arbitrary edge and walk in both directions.

Since %neighbour is symmetric this shouldn't be a problem, just swap the orientation of the start segment.

I'm on mobile and I want you to understand the algorithm...so no code. :)

Cheers Rolf

( addicted to the Perl Programming Language)