Graph Interpretation
When dealing with garbage collection schemes, it's often helpful to think of the reference graph, which is a directed graph where the vertices are objects and there is an edge from an object A to an object B if A holds a reference to B. We also have a special vertex or vertices representing the local variables and references held by the runtime system, and no edges ever go to these nodes, although edges can go from them to other nodes.
In this context, the simple reference count of an object is the in-degree of its vertex. Deleting a vertex is like collecting an object. It can only be done when the vertex has no incoming edges, so it does not affect the out-degree of any other vertices, but it can affect the in-degree of other vertices, causing their corresponding objects to be collected as well.
The connected component containing the special vertex contains the objects that can't be collected, while other connected components of the graph only contain garbage. By the nature of reference counting, each of these garbage components must contain at least one cycle.
Read more about this topic: Reference Counting
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