Concept mapping has been widely used as one of the most efficient methods of revealing the cognitive structure of an individual on any concept. There are not only different concept mapping techniques but also different ways of analysis. It has been suggested that concept maps provide valuable and rich information which becomes disoriented when they are analyzed only quantitatively. This study has described a qualitative analyzing method of concept maps, developed for investigating the cognitive structures of preservice teachers on some educational concepts. An analysis of the relations between the concepts in concept maps is developed and discussed which was neglected by both qualitative and quantitative analyses in the literature. This analyzing method aims to examine concept maps created by pre-service teachers using "construct-a-map-from-scratch" method centred on multiple key concepts which emphasized the categorization of linkage labels and other connected concepts. (Contains 3 tables and 3 figures.)