Diictodons lived in pairs, and burrowed near each other, though it wasn't a colony. They constantly competed for food, but they did notify each other (possibly accidently) of predators nearby (such as Gorgonops). Diictodons probably didn't kill each other as they competed for food, but may have attacked each other lightly, causing small cuts. I theorize that Diictodon verbally communicated, due to the fact that they had advanced ear structures.
A group of diictodons roam across the permian deserts, searching for tubers to consume.