End-to-end　learned　image　compression　exploits　the　expressive　power　of　nonlinear　transform　modules　to　de-correlate　the　spatial　redundancies　of　image　contents.　Due　to　its　long-range　attention　scheme,　transformer-based　transforms　can　explore　more　global　features　for　better　reconstruction.　However,　transformer　modules　bring　in　indispensable　computational　costs,　and　the　coarse　utilization　of　transformer　in　learned　image　compression　cannot　meet　the　coding　efficiency.　In　this　paper,　we　propose　a　novel　graph-structured　swin-transformer　for　learned　image　compression,　shown　in　Figure　1.　We　assume　that　the　global　receptive　field　of　attention　map　should　be　sparse　not　dense,　while　the　local　neighboring　correlations　must　be　strong.　　©　2024　IEEE.