Editing Reference counting (section)

==Graph interpretation==
When dealing with garbage collection schemes, it is often helpful to think of the '''reference graph''', which is a [[directed graph]] where the [[vertex (graph theory)|vertices]] are objects and there is an edge from an object&nbsp;A to an object&nbsp;B if A holds a reference to&nbsp;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 if their in-degree also becomes 0 as a result.

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. If a reference-counting garbage collection algorithm is implemented, then each of these garbage components must contain at least one cycle; otherwise, they would have been collected as soon as their reference count (i.e., the number of incoming edges) dropped to zero.