I am learning about some of the common applications of Markov random fields (a.k.a. undirected graphical models) to data science. A common feature of many applications I have read about is that the number of variables in the model is relatively large (e.g. in applications to computer vision or NLP). For educational purposes, I am interested in the following question:
Are there nice examples of MRF models where the number of variables in the model is very small (i.e. $<10$)?
Ideally, such examples would have some practical use. I would like more than just a toy model graph labelled with some variables (a real model based on a real data set is what I'm looking for).
As a follow up:
If no, why not? Is there something about MRF that makes modelling small numbers of variables uninteresting? Are other types of models preferred in that case for some reason? If yes, please elaborate on the example.