Sleep　is　crucial　for　human　health.　Automatic　sleep　stage　classification　based　on　polysomnography　(PSG)　is　meaningful　for　the　diagnosis　of　sleep　diseases,　which　has　attracted　extensive　attention　recently.　Most　existed　works　learn　the　representations　of　PSG　based　on　the　conventional　grid　data　structure,　ignoring　the　topological　channel　correlations　among　different　body　regions　in　non-Euclidean　space.　To　this　end,　we　propose　a　deep　learning　model　named　SAGSleepNet,　which　transforms　PSG　into　a　robust　graph　structure　by　neural　networks　and　self-attention　mechanism,　utilizing　graph　convolution　network　(GCN)　and　bidirectional　gated　recurrent　unit　(BiGRU)　to　capture　epoch-level　topological　channel　correlations　and　sequence-level　temporal　sleep　transitions　of　PSG,　respectively.　The　final　learned　representation　is　fed　into　a　softmax　layer　to　train　an　end-to-end　model　for　automatic　sleep　staging.　Experimental　results　on　three　public　datasets　(i.e.,　SleepEDFx,　UCD,　CAP)　show　that　SAGSleepNet　obtains　the　best　classification　performance　compared　with　several　baselines,　including　accuracy　of　0.807,0.765,　and　0.746,　F1-score　of　0.744,　0.750,　and　0.695,　and　Cohen＇s　Kappa　(kappa)　of　0.721,　0.690,　and　0.660.　In　general,　our　work　provides　a　reasonable　graph　structure　to　model　PSG　epoch,　and　makes　contribution　to　explore　implicit　channel-wise　information　of　PSG　by　deep　learning　techniques.