Mathematics educators and mathematics standards of curriculum have emphasised the importance of constructing the interconnectedness among mathematic concepts ("conceptual understanding") instead of only the ability to carry out standard procedures in an isolated fashion. Researchers have attempted to assess the knowledge networks in students' minds. A technique that has gained popular use in science education over the past three decades is concept mapping. This paper examines students' conceptual understanding about triangle concepts using concept maps, and an analysis of the maps using degree centralities derived from social network analysis has demonstrated new insights through this novel technique. (Contains 1 figure and 3 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]