Miscellanea. On the generation of the chordless four-cycle

In the theory of Markov graphical representations of conditional independencies a special role is played by the chordless four-cycle, representing for four random variables the conditional independencies X ⊥⊥ V|(U, W) and W ⊥⊥ U|(X, V). It is not immediately clear how such systems are to be generated. Here we sketch some possible data-generating mechanisms.