Borrowing from Laurent_R's answer, you might want to consider using Graph::Undirected to get the connections. I also borrowed this graph example from somewhere, probably from here at Perl Monks but can't find the original in a search.

#!/usr/bin/perl
use strict;
use warnings;
use Graph;

my $g = Graph::Undirected->new;

while (<DATA>) {
    chomp;
    my ($x, $y) = split /;/;
    $y = $x if $y eq ''; # will pass $y == 0 if that's the case
    $g->add_edge($x, $y);
}

my %pred;

for my $aref ($g->connected_components) {
    my @items = sort {$a <=> $b} @$aref;
    my $first = $items[0];
    for my $element (@items) {
        $pred{$element} = $first;    
    }    
}

print "$_ => $pred{$_}\n" for sort {$a <=> $b} keys %pred;

__DATA__
567;456
456;345
345;234
234;123
339;228
228;117
131;
435;324
324;213
372;
[download]

Prints:

117 => 117
123 => 123
131 => 131
213 => 213
228 => 117
234 => 123
324 => 213
339 => 117
345 => 123
372 => 372
435 => 213
456 => 123
567 => 123
[download]

Update: Changed $g->add_edge($x, $y || $x); to $g->add_edge($x, $y); and added $y = $x if $y eq ''; so to allow $y to be a possible zero.