Concept maps have been adopted extensively in teaching and assessment. Assessment schemes, including the closeness index and the N-G method, have also been widely applied to evaluate the quality of students’ concept maps. Teachers must make great efforts to evaluate students’ concept maps, because present concept map assessment schemes do not reveal ways to help them improve such maps. Additionally, teachers cannot easily provide constructive suggestions to students to improve their learning, particularly when concept maps incorporate many concepts and links. This work presents linkage algorithms that can be used to discover the patterns (such as confused concepts, substitute concepts, and hidden wrong concepts) in concept maps to support assessment. Teachers can use the discovered patterns not only to become aware of the conceptions of students, but also to improve students’ conceptions efficiently.