Sparse feature matching poses three challenges to graph-based methods: (1) the combinatorial nature makes the number of possible matches huge; (2) most possible matches might be outliers; (3) high computational complexity is often incurred. In this paper, to resolve these issues, we propose a simple, yet surprisingly effective approach to explore the huge matching space in order to significantly boost true matches while avoiding outliers. The key idea is to perform mode-seeking on graphs progressively based on our proposed guided graph density. We further design a density-aware sampling technique to considerably accelerate mode-seeking. Experimental study on various benchmark data sets demonstrates that our method is several orders faster than the state-of-the-art methods while achieving much higher precision and recall. 2014 Springer International Publishing.