Here is the table I have created by testing the closure table method.

|    id    |    parentId    |    childId    |    hops
|          |                |               |
|    270   |       6        |       6       |      0
|    271   |       7        |       7       |      0
|    272   |       8        |       8       |      0
|    273   |       9        |       9       |      0
|    276   |       10       |       10      |      0
|    281   |       9        |       10      |      1
|    282   |       7        |       9       |      1
|    283   |       7        |       10      |      2
|    285   |       7        |       8       |      1
|    286   |       6        |       7       |      1
|    287   |       6        |       9       |      2
|    288   |       6        |       10      |      3
|    289   |       6        |       8       |      2
|    293   |       6        |       9       |      1
|    294   |       6        |       10      |      2

I am trying to create a simple tree of this using PHP. There does not seem to be enough data to create the table. For example, when I look purely at parentId = 6:

-Part 6 
 -Part 7
  - ?
   - ?
 -Part 9 
   - ?
    - ?

We know that parts 8 and 10 exists below Part 7 or 9, but not which. We know that part 10 exists at both 3 and 4 nodes deep but where?

If I look at other data in the table it is possible to tell it should be:

- Part 6 
 - Part 7
  - Part 9
   - Part 10
 - Part 9
  - Part 10

I thought one of the benefits of closure tables was there was no need for recursive queries? Could you help explain what I am doing wrong?

EDIT: For clarification, this is a mapping table. There is another table called "parts" which has a column called part_id that correlates to both the parentId and childId columns in the "closure" table. The "id" column in the table above (closure) is just for the purposes of maintaining a primary key. It is not really necessary. The methods I have used to create this closure table is described in the following article: http://dirtsimple.org/2010/11/simplest-way-to-do-tree-based-queries.html

EDIT2: It can have two and three hops. I will explain easier by assigning names to the items.

Part 6 = Bicycle
Part 7 = Gears
Part 8 = Chain
Part 9 = Bolt
Part 10 = Nut

Nut is part of Bolt. The Bolt and Nut combo exists directly within Bicycle and within Gears which is part of Bicycle.

In relation to what method to use I have looked at Adjacency, Edges, Enum Paths, Closures, DAGS(networks) and the Nested Set Model. I am still trying to work out what is what, but this is an extremely complex component database where there are multiple parents and any modification to a sub-tree must propogate through the other trees. More importantly there will be insertions, deletions and tree views that I wish to avoid recursion during general use, even at the cost of database space and query time during entry.