The　flexible　job　shop　scheduling　(FJSS)　is　important　in　real-world　factories　due　to　the　wide　applicability.　FJSS　schedules　the　operations　of　jobs　to　be　executed　by　specific　machines　at　the　appropriate　time　slots　based　on　two　decision　steps,　namely,　the　job　sequencing　(i.e.,　the　sequence　of　jobs　executed　on　a　machine)　and　the　job　routing　(i.e.,　the　route　of　a　job　to　a　machine).　Most　current　studies　utilize　either　deep　reinforcement　learning　(DRL)　or　multi-agent　reinforcement　learning　(MARL)　for　FJSS　with　a　large　search　space.　However,　these　studies　suffer　from　two　major　limitations:　no　integration　between　DRL　and　MARL,　and　independent　agents　without　cooperation.　To　this　end,　we　propose　a　new　model　for　FJSS,　called　DeepMAG　based　on　Deep　reinforcement　learning　with　Multi　-Agent　Graphs.　DeepMAG　has　two　key　contributions.　(1)　Integration　between　DRL　and　MARL.　DeepMAG　integrates　DRL　with　MARL　by　associating　a　different　agent　to　each　machine　and　job.　Each　agent　exploits　DRL　to　find　the　best　action　on　the　job　sequencing　and　routing.　After　a　job-associated　agent　chooses　the　best　machine,　the　job　becomes　a　job　candidate　for　the　machine　to　proceed　to　its　next　operation,　while　a　machine-associated　agent　selects　the　next　job　from　its　job　candidate　set　to　be　processed.　(2)　Cooperative　agents.　A　multi-agent　graph　is　built　based　on　the　operation　relationships　among　machines　and　jobs.　An　agent　cooperates　with　its　neighboring　agents　to　take　one　cooperative　action.　Finally,　we　conduct　experiments　to　evaluate　the　performance　of　DeepMAG　and　experimental　results　show　that　it　outperforms　the　state-of-the-art　techniques.(c)　2022　Elsevier　B.V.　All　rights　reserved.