Digital　Twin　Network　(DTN)　constructs　a　many-to-many　mapping　network　by　communicating　and　collaborating　with　massive　Digital　Twins　(DTs),　which　can　better　assist　the　management　and　operation　of　large-scale　modern　systems.　However,　the　emergence　of　DTN　mirrors　a　growing　demand　for　bulk　data　transfer　between　geo-distributed　DT　nodes　in　the　physical　network　infrastructure.　Conventional　end-to-end　connections　are　facing　a　great　challenge　in　the　presence　of　the　background　traffic　fluctuation.　In　this　paper,　we　propose　a　graph　convolutional　network　(GCN)-enabled　scheduling　method　to　schedule　bulk　data　transfers　across　the　DTN　in　a　store-and-forward　(SnF)　manner.　Instead　of　solving　the　complex　SnF　scheduling　problem　on　the　entire　network,　the　proposed　method　decomposes　the　problem　into　multiple　sub-problems　on　different　pre-computed　routes.　Instead　of　learning　the　scheduling　results　directly,　the　GCN　model　is　used　to　predict　the　reachability　of　DT　nodes.　These　unreachable　nodes　will　be　excluded　from　the　scheduling　process.　Our　studies　show　that　the　proposed　method　obtains　better　network　performance　and　lower　complexity　when　compared　with　the　conventional　scheduling　methods.　©　2023　IEEE.