[eru]

Well, you need to be careful what your graph and nodes are supposed to model.

I was implicitly assuming that your graph models instructions and procedures. You seem to assume that the graph models concrete physical items.

You can execute the same steps twice, but you can't eat the same piece of butter twice.

[xnorswap]

It's a bit philosophical, but I'm not sure you can really execute the same steps twice. A cycle would imply you can get stuck baking something forever.

When you come back to do the "same" operation again, you're fundamentally dealing with different items, even if it doesn't appreciably appear to be the case.

You might have different criteria for evaluation, but something has fundamentally changed.

Let's look at the simplest case you might be tempted to model as a cycle:

> "Salt to taste"

Now, that would traditionally be modelled in a flowchart as a cycle:

1. Add salt

2. Test taste. Too little salt? Go to step 1. Else go to step 3.

3. End.

However, in strict modelling terms, I'd argue there's a hidden parameter, "number of saltings attempted".

You wouldn't repeat that a hundred times and keep adding salt, after a while you'd suspect that your taste-buds had gone or the salt had gone funny.

So rather than a cycle, it's actually a series of steps with a hidden step counter, which eventually has different outcomes.

[eru]

I'm glad you figured out that the graph is a model, and like any good model, it picks some characteristics of reality to keep and many to leave out.

Have a look at the example of a turnstile state machine on Wikipedia: https://commons.wikimedia.org/wiki/File:Turnstile_state_mach...

The graph of that state machine suggests that you repeat the cycles indefinitely. But I have it on good authority that real world turnstiles only have a finite coin box. [citation needed] So there's some extra hidden state.