I feel I might not understand what you actually want from your question. Even though, this answer might be way off from what you need, it should be beneficial to you to remind you of the diversity and complexity of relationships you have to consider.
I am tempted to urge you to perceive this as a mathematical issue concerning topology and sets.
Perhaps, you might already be aware ...
Your first concern is commutativity.
If A operand B produces the same result as B operand A, than operand is commutative.
- A plus B = B plus A. Addition is a commutative operand.
- A divided by B is not the same as B divided by A. Division is not commutative.
Next is membership. For example
- B is a member of A.
- C is child of D.
- E1 is a dependent of E2.
- His concept is an extension of mine.
- Area is the integral of a shape.
- Acceleration is a derivative of velocity.
We might also have to consider referential relationship or indirection.
- A references B
- Jonathan is the name of her brother.
- This is a copy of the original
- X population is correlated to Y population
Symmetrical relationship is a loaded term. You should try to use the term non-commutative relationship when you actually mean so.
For example, these are symmetrical relationships
- There are as many houses as there are cars per owner.
- A friend of yours is a friend of mine
These are asymmetrical relationships:
- For inflation to occur, demand must outstrip supply.
- There are more women than men in the world.
There should not exist a single term you could use to abstract the relationships you might wish to describe.
Therefore, the following could be used to genericize a relationship from revealing if it is a parent-child or child-parent, plus or minus or divide, etc
- A and B are in a non-commutative interaction.
- There exists a dependency between C and D.
- The dynamics between rich and poor are asymmetric.
- There is correlation between the two occurrences.
- A complementary relationship exists
I realise you might insist on being given some prepositional clauses. Therefore having the comprehension of the diversity of relationships, here are examples
- Women were correlated against men in the survey.
- Racial equal-opportunities were contraindicated by the survey.
- Process A is dependent on process B.
- Process C is consequent to process D.
- The contradiction was commuted by the presence of your solution.
- The election results indicate asymmetric preference of the public towards Republicans and Democrats
- In China, there is asymmetric preference between having male and female babies.
- There is a sense of indirection among the various clans when it comes to who is actually in charge of the village.