Here's my non Graph::Traversal solution. Still looking for something simpler and cleaner with ::Traversal fi someone can help thanks

#!/usr/bin/perl -w
use strict;
use warnings;
use diagnostics;
use Graph;
use Graph::Traversal::DFS;


my $g = Graph->new();
$g->add_edges ( ['A', 'B'], ['B', 'C'], ['C', 'D'], ['D', 'K'], ['D', 
+'Z'], ['K', 'R'] );

my @source = $g->source_vertices;

foreach ( @source )
{
    DFS($_);
    print qq[\n\n];
}


sub DFS
{
    my $start_node = shift;
    my @queue = ($start_node);
    my @paths;

    while(scalar(@queue) > 0)
    {
        my $node = pop(@queue);
        my @next_nodes;

        if ( index $node, ':' )
        {
            my @n = split ':', $node;
            my $nnode = $n[-1];
            @next_nodes = $g->successors($nnode);
        }

        else
        {
            @next_nodes = $g->successors($node);
        }

        @next_nodes = map { "$node".':'."$_" } @next_nodes;
        push @paths, $_ foreach @next_nodes;
        push @queue, @next_nodes;
    }

    for my $path ( @paths )
    {
        print qq[$path\n];
    }

}
[download]

A:B

A:B:C

A:B:C:D

A:B:C:D:Z

A:B:C:D:K

A:B:C:D:K:R