Single　image　dehazing　algorithms　aim　to　recover　a　clear　image　from　a　hazy　one.　Most　learning-based　single　image　dehazing　algorithms　are　trained　on　synthetic　datasets　and　have　limited　inference　ability　to　real-world　scenes.　We　propose　a　graph-disentangled　representation　based　semi-supervised　single　image　dehazing　algorithm　(GDSDN).　Specifically,　a　graph-disentangled　representation　network　is　presented　to　decouple　the　content　and　mask　features,　and　the　decoupled　content　features　are　employed　to　reconstruct　dehazed　results.　In　addition,　the　interaction-reconstruction　strategy　and　contrastive　loss　are　designed　to　constrain　the　disentangled　content　and　mask　features.　Extensive　experimental　results　on　synthetic　and　real-world　images　show　that　our　model　achieves　competitive　results.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.