This paper presents a graph-theoretic approach for interactive region-based image retrieval. When dealing with image matching problems, we use graphs to represent images, transform the region correspondence estimation problem into an inexact graph matching problem, and propose an optimization technique to derive the solution. We then define the image distance in terms of the estimated region correspondence. In the relevance feedback steps, with the estimated region correspondence, we propose to use a maximum likelihood method to re-estimate the ideal query and the image distance measurement. Experimental results show that the proposed graph-theoretic image matching criterion outperforms the other methods incorporating no spatially adjacent relationship within images. Furthermore, our maximum likelihood method combined with the estimated region correspondence improves the retrieval performance in feedback steps.