It’s not at all common among Bayesian statisticians. Not really a single complete example in Gelman et al.'s textbooks, for example, though he does draw some partial ones in chapter 5 of Bayesian Data Analysis for hierarchical models. Statisticians will write down graphical models precisely using sampling notation, which is precise, but they’ll rarely write out a sketchy diagram that only partly describes the model. Computer scientists, in contrast, will insist on the sketchy diagrams, as I have learned from reviewers.
Here, “conditional variances” is a typo here and should have been “conditional distributions”.
For Gibbs sampling, the graphical operations calculate the Markov blankets of a node in the network to find all the variables that are involved in its conditional distribution. This notion was introduced by Pearl in the 1980s. This is what both BUGS and JAGS did and what NIMBLE still does. Since PyMC is largely graphical modeling based and has discrete sampling, I assume it calculates Markov blankets somewhere internally.
There’s complete documentation with BUGS in the early 1990s. Presumably Pearl had precise definitions. You can find everything you need in Kohler and Friedman’s book on graphical models from the 00s.