To compress a graph, some methods rely on finding highly compressible structures, such as very dense subgraphs, and encode a graph by listing these structures compressed. However, structures can overlap, leading to encoding the same information multiple times. The method we propose deals with this issue, by identifying overlaps and encoding them only once. We have tested our method on various realworld graphs. The obtained results show that our approach is efficient and outperforms state of the art methods. The source code of our algorithms, together with some sample input instances, are available at https://gitlab.liris.cnrs.fr/fpitois/fgsp.git.