Transitive-Closure Table Restructure - mysql

Question

How would I be able to retrieve a full-tree from the current structure, or refactor the current table structure to allow for an optimized recursive query?
Issue
Unable to retrieve full-tree of components from base component without iteration.
A single component can have an undefined number of connections (depth).
Components do not have a parent property, as each component can be related to multiple components.
Unable to recursively update affected attribute values of a component.
For example if the price of a component changes, the price is updated for all related components_of.
Current Structure
component
primary key (id)
| id | price |
|----|------ |
| A | 1 |
| B | 1 |
| C | 1 |
| D | 2 |
| E | 2 |
component_closure
unique index (component, component_of)
index (component_of)
FK (component) References component (id)
FK (component_of) References component (id)
| component | component_of |
|--------------------------|
| D | B |
| D | C |
| B | A |
| E | C |
| E | A |
Resulting Graph Model:
Example query:
UPDATE component
SET price = 2
WHERE id = 'A';
Desired Result (* indicates recursively updated values)
| id | price |
|----|------ |
| A | 2 |
| B | 2 | *
| C | 1 |
| D | 3 | *
| E | 3 | *
I am thinking I would need to store the entire tree relationship in the component_closure table, so that I would be able to retrieve the component_of relationships of all components and use a depth column to determine the order of components. Though that seems wasteful when the full-tree is not needed, such as for immediate components_of.
For example:
| component | component_of | depth |
|-----------|--------------|-------|
| D | A | 1 |
| D | B | 2 |
| D | C | 1 |

Answer 1

Yes, if you want to store the transitive closure, you need to store all paths.
For some operations, it's even helpful to store the path of length 0:
| component | component_of | depth |
|-----------|--------------|-------|
| D | D | 0 |
| D | A | 1 |
| D | B | 2 |
| C | C | 0 |
| B | B | 0 |
| B | A | 1 |
| A | A | 0 |
In MySQL 8.0, none of this will be needed. We'll finally be able to use recursive queries.