# Term for a 'flat' circuit in a graph

Graphs can contain circuits, i.e. paths which start and end at the same node. Most circuits are 'non-flat', like this:

I'm trying to find a term that describes a particular type of circuit. You might describe it as 'flat', 'zero-volume' or 'doubling-back'.

The circuit visits some nodes in the following order: $$[n_{1}, n_{2}, \dots, n_{x-1}, n_{x}, n_{x-1}, \dots, n_{2}, n{1}]$$.

Here's an illustration of the same concept:

• A simple graph has undirected edges, and only a single edge between any two vertices. So, among simple graphs, any path could be deemed a 'flat' circuit, should you so choose. A directed graph similarly tends to have a single edge between any two vertices. But, that edge may be unidirectional or bidirectional. If every edge is bidirectional, then every path yields a 'flat' circuit. So, it is not entirely clear what you are looking for. Depending on the context, there could be more than one name for what you want. Apr 22, 2020 at 12:22