Extracting concepts from fulltext data collections is a daunting task in that many different concepts and themes are intertwined and ample term variation exists in fulltext. Concepts represent topics or themes of a article and are helpful means of managing and searching large document collections. In addition, automatically extracting and assigning concepts play a pivotal role in indexing electronic documents and building digital libraries. In this paper we propose a novel approach to biomedical concept extraction by adopting a ranking algorithm of relative importance in concept graphs. The proposed consists of two major steps: First, we represent full-text documents by graphs whose nodes and edges are determined by named entity recognition and UMLS Semantic Network. Second, we rank concepts with relative importance algorithms. We evaluate our technique with a set of biomedical full-texts and compare it to various different key-phrase extraction and graph ranking techniques. The experimental results show that our technique achieves the best performance over other compared algorithms.