Are cycles possible in circuits of neurons? If we consider neurons nodes and connections between them edges, are cycles (from graph theory) are possible in the brain?

To put it another way, would the signal generated from neuron1 be able to travel around in a circuit of other neurons and come back to activate neuron1 again? Or is this generally not possible because neuron1 would still be recovering/re-potentiating?

If yes, as a programmer I would expect this to be the mechanism by which contiguous experience would be possible (ie. the main event loop of an application). Any studies/field/reseachers you could point me to for further research?
There are tons of cycles in the brain. The study of how the brain uses these cycles are used for computation is called Theoretical Neuroscience. Browsing the tag on this website is one way to become introduced to those ideas.

Alternatively, these loops are framed in different ways in "How to Build a Brain" by Chris Eliasmith. Loops involving a population node connecting to itself are considered to be memories. Longer loops, such as the basal-ganglia$\rightarrow$thalamus$\rightarrow$cortex loop could be considered analogous to the "main event loop" of a program, but with a few caveats.