While a directed graph structure is suitable for a set of random variables where there is clear causality, an undirected graph structure is better fit for a situation where dependence upon random variables flows in multiple directions.

For example, a model showing the health status (probability of having a cold) of you, your roommate, and a coworker could be represented with an undirected graph. Your health status would be a node with undirected vertices connected to your coworker's and roommate's health status respectively, as you can get either of them sick, either one of them could get you sick, but they cannot directly get each other sick.