Context:　Code　readability　is　crucial　for　developers　since　it　is　closely　related　to　code　maintenance　and　affects　developers’　work　efficiency.　Code　readability　classification　refers　to　the　source　code　being　classified　as　pre-defined　certain　levels　according　to　its　readability.　So　far,　many　code　readability　classification　models　have　been　proposed　in　existing　studies,　including　deep　learning　networks　that　have　achieved　relatively　high　accuracy　and　good　performance.　Objective:　However,　in　terms　of　representation,　these　methods　lack　effective　preservation　of　the　syntactic　and　semantic　structure　of　the　source　code.　To　extract　these　features,　we　propose　a　graph-based　code　representation　method.　Method:　Firstly,　the　source　code　is　parsed　into　a　graph　containing　its　abstract　syntax　tree　(AST)　combined　with　control　and　data　flow　edges　to　reserve　the　semantic　structural　information　and　then　we　convert　the　graph　nodes’　source　code　and　type　information　into　vectors.　Finally,　we　train　our　graph　neural　networks　model　composing　Graph　Convolutional　Network　(GCN),　DMoNPooling,　and　K-dimensional　Graph　Neural　Networks　(k-GNNs)　layers　to　extract　these　features　from　the　program　graph.　Result:　We　evaluate　our　approach　to　the　task　of　code　readability　classification　using　a　Java　dataset　provided　by　Scalabrino　et　al.　(2016).　The　results　show　that　our　method　achieves　72.5%　and　88%　in　three-class　and　two-class　classification　accuracy,　respectively.　Conclusion:　We　are　the　first　to　introduce　graph-based　representation　into　code　readability　classification.　Our　method　outperforms　state-of-the-art　readability　models,　which　suggests　that　the　graph-based　code　representation　method　is　effective　in　extracting　syntactic　and　semantic　information　from　source　code,　and　ultimately　improves　code　readability　classification.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.