This book constitutes the thoroughly refereed post-conference proceedings of the Third International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2013, held in Beijing, China, in August 2013, associated with IJCAI 2013, the 23rd International Joint Conference on Artificial Intelligence. The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers feature current research involved in the development and application of graph-based knowledge representation formalisms and reasoning techniques. They address the following topics: representations of constraint satisfaction problems; formal concept analysis; conceptual graphs; and argumentation frameworks.