The notion of relevance that is very important in knowledge based systems can be efficiently encoded by conditional independence. Although directed acyclic graphs (DAG) are powerful means for representing conditional independencies in probability distributions it is not always possible to find a DAG that represents all conditional independencies and dependencies of a distribution. We present a new formalism that is able to do this for positive probability distributions. The main issue is to augment a DAG with a special kind of arcs that induce independencies. Furthermore, an efficient algorithm is presented for building these extended DAGs.