Rule-based representation techniques have become popular for storage and manipulation of domain knowledge in expert systems. It is important that systems using such a representation are verified for accuracy before implementation. In recent years, graphical techniques have been found to provide a good framework for the detection of errors that may appear in a rule base. The authors present a graphical representation scheme that: 1) captures complex dependencies across clauses in a rule base in a compact yet intuitively clear manner and 2) is easily automated to detect structural errors in a rigorous fashion. Their technique uses a directed hypergraph to accurately detect the different types of structural errors that appear in a rule base. The technique allows rules to be represented in a manner that clearly identifies complex dependencies across compound clauses. Subsequently, the verification procedure can detect errors in an accurate fashion by using simple operations on the adjacency matrix of the directed hypergraph. The technique is shown to have a computational complexity that is comparable to that of other graphical techniques. The graphical representation coupled with the associated matrix operations illustrate how directed hypergraphs are a very appropriate representation technique for the verification task.