We present a fully unsupervised, extractive text summarization system that leverages a submodularity framework introduced by past research. The framework allows summaries to be generated in a greedy way while preserving near-optimal performance guarantees. Our main contribution is the novel coverage reward term of the objective function optimized by the greedy algorithm. This component builds on the graph-of-words representation of text and the k-core decomposition algorithm to assign meaningful scores to words. We evaluate our approach on the AMI and ICSI meeting speech corpora, and on the DUC2001 news corpus. We reach state-of-the-art performance on all datasets. Results indicate that our method is particularly well-suited to the meeting domain.