Is there a name for a cycle without subcycles

Question

My question is quite simple and is in the title: Is there a name for a cycle without subcycles (in directed graph)?

For my research (in economics, not math, but I need these tools) I am interested in those objects, and I was wondering if they have a specific name? I know it is not elementary nor simple cycles.

Here is a example of what I mean: I have a a graph with the following edges:

• a->b
• b->c
• c->d
• d->a
• c->a

There are two cycles here:

• abcda
• abca

Here I would like to know what would be the name of a cycle without inside cycles, that is, the cycle abca?

Thank you for your help!

Answer 1

This is variously called simple cycle, circle, circuit, or polygon. See the Wikipedia article on cycles.

A polynomial algorithm for finding mininum circuits in directed graphs was given by Itai and Rodel, SIAM J. Computing 1978.