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Algorithm for counting possible simulations #23

@jmorris335

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@jmorris335

The number of actual simulations (not maximum but defined) for a hypergraph can be found by evaluating chains. You're really looking for the number of paths in the hypergraph, with every edge representing the smallest unit of path you can simulate. For an ordered chain of edges, the formula for number of sims is simply:

$$\sum_{i=0}^{n-1} n-i \equiv \sum_{i=0}^{n} n-i$$

Where n is the length of the chain. When a chain branches, you still calculate the paths for the whole chain, but then you have to minus the parts of the chain that were already counted. It would be nice to have an algorithm that did this for an arbitrary hypergraph, though I'm not sure what utility it would have other than scientific analysis of the CHG.

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