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I'm currently studying computer science, and we recently started doing graph theory.

My question: what is the name of the field of graph theory, where the existence of edges is determined by which edges have already been traversed, or by some other condition? For example:

Node 1 -Edge1-> Node 2 -Edge2-> Node 3,

You can only traverse Edge2 if edge 1 was traversed beforehand. This is a very simple example, but I'm interested in seeing where this has been applied on a larger scale.

Sorry if this is a very simple question!

Thanks!

Nikita

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    I'm still confused about the property that you want. Here's why: if edges exist only after other (incident?) edges are traversed then where did the first edge come from? I think that formulating the property differently would be helpful. Are you wanting a directed graph so that there exists a single walk along all the edges? Is there any kind of restriction to this walk (i.e. visiting vertices / edges once)? – 2017-01-03
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    @ChrisHarshaw Existed is definitely the wrong word. What I mean, is that some edges can only be traversed after having traversed a specific edge beforehand. For now I'm not concerned with restrictions on the edges. – 2017-01-04

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I am not an expert, but this seems like it could be modeled with a colored Petri Net. Hopefully someone more versed in Petri Nets will confirm or deny this.