Ok, first to get the terminology straight, 'node' eq 'vertex' and 'edge' eq 'link'.

In your code both nodes and links have an id. Let's look at your original code:

# this marks the current vertex
$explored->{$node->{_id}}++;

foreach my $link (@{$node->{_outlinks}}) {
   # $link isa Link, so $link->{_id} is the id of the link,
   # not of the vertex!!
   $do_search->($link->{_to}) unless ($explored->{$link->{_id}});
}
[download]

Yes, your algorithm is fine, it's just the implementation that has a little bug in it. Here's my (correct) code again, this time written explicitly:

$explored->{$node->{_id}}++;
foreach my $link (@{$node->{_outlinks}}) {
   my $new_node = $link->{_to};
   $do_search->($new_node) unless ($explored->{$new_node->{_id}});
}
[download]