roboticus,
Thank you. I have a real hard time thinking recursively for some reason. There are some things that I would want to change. For instance, letting the call stack be handled automatically by the recursion and not relying on lexicals visible at the package level. Here is my take on satisfying those two changes:

my %net = (...); # shortened for brevity sake

print find_path('1.2.3.4', '1.2.3.6', \%net);
sub find_path {
    my ($beg, $end, $net, $seen, $stop, $node, $path) = @_;

    if (! defined $stop) {
        ($node, $path) = ($beg, $beg);
        $stop->{$_} = 1 for @{$net->{$end}};
    }
    return $path if $node eq $end;
    return "$path=>$end" if $stop->{$node};
    return undef if $seen->{$node}++;

    for (@{$net->{$node}}) {
        my $found = find_path($beg, $end, $net, $seen, $stop, $_, "$pa
+th=>$_");
        return $found if $found;
    }
    return 'path not found';
}
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I liked the iterative solution better because I could alter the search process by adjusting the shift/unshift and push/pop. I thought recursive solutions were supposed to be more elegant. Perhaps it is just because I don't know what I am doing.