We propose a novel approach for unsupervised extractive summarization. Our approach builds a semantic graph for the document to be summarized. Summary extraction is then formulated as optimizing submodular functions defined on the semantic graph. The optimization is theoretically guaranteed to be near-optimal under the framework of submodularity. Extensive experiments on the ICSI meeting summarization task on both human transcripts and automatic speech recognition (ASR) outputs show that the graph-based submodular selection approach consistently outperforms the maximum marginal relevance (MMR) approach, a concept-based approach using integer linear programming (ILP), and a recursive graph-based ranking algorithm using Google's PageRank.