Identifying compelled edges is important in learning the structure (i.e., the DAG) of a Bayesian network. A graphical method (Chickering 1995) was proposed to solve this problem. In this paper, we show that a joint probability distribution defined by a Bayesian network can be uniquely characterized by its intrinsic factorization. Based on such an algebraic characterization, we suggest a simple algorithm to identify the compelled edges of a Bayesian network structure. 1