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, $_, "$path=>$_");
        return $found if $found;
    }
    return 'path not found';
}