How do I detect circular logic or recursion in a multi-levels references and dependencies

Question

I have a graph of multi-level dependecies like this, and I need to detect any circular reference in this graph.

A = B

B = C

C = [D, B]

D = [C, A]

Somebody have a problem like this?

Any solution???

Thanks and sorry by english.

========= updated ==========

I had another situation.

1

2 = 1

3 = 2

4 = [2, 3]

5 = 4

In this case, my recursive code iterate two times in "4" reference, but this references don't generate a infinite loop. My problem is to know when function iterate more than one time a reference and is not infinite loop and when is a infinite loop, to inform user.

1 = 4

2 = 1

3 = 2

4 = [2, 3]

5 = 4

This case is a bit diferent from 2th example. This generate a infinite loop. how can I know when cases generate a infinite loop or not?

Answer 1

Topological sorting. The description on Wikipedia is clear and works for all your examples.

Basically you start with a node that has no dependencies, put it in a list of sorted nodes, and then remove that dependency from every node. For you second example that means you start with 1. Once you remove all dependencies on 1 you're left with 2. You end up sorting them 1,2,3,4,5 and seeing that there's no cycle.

For your third example, every node has a dependency, so there's nowhere to start. Such a graph must contain at least one cycle.