Unsupervised　clustering　is　a　crucial　issue　in　data　mining　and　pattern　recognition.　Based　on　deep　learning　paradigms,　deep　clustering　algorithms　have　been　studied　extensively　and　obtained　superior　performance　in　various　applications.　However,　most　of　previous　methods　did　not　use　helpful　information　from　neighborhood　relations　to　form　group-separated　space,　and　the　feature　embedding　is　usually　distorted　during　the　training　process.　To　tackle　the　former　limitation,　we　develop　a　graph　convolution　based　unsupervised　learning　algorithm　named　Stacked　Graph　Autoencoder　(SGAE).　Specifically,　SGAE　utilizes　the　message　passing　mechanism　to　aggregate　information　from　neighbors　and　obtain　a　meaningful　and　separated　latent　representation.　Since　the　adjacency　matrix　is　unavailable　in　clustering　tasks,　a　graph　construction　approach　with　two　pruning　strategies　is　introduced　to　generate　a　transition　matrix.　To　reduce　the　distortion　caused　by　the　multi-layered　network　training　process,　we　further　propose　a　topological　structure　preservation　mechanism.　It　uses　the　constructed　adjacency　graph　as　supervised　information,　to　maintain　the　relationship　between　nodes　in　the　original　space.　Experiments　on　several　popular　benchmark　datasets　show　that　SGAE　achieves　significant　improvements　compared　to　unsupervised　and　semi-supervised　deep　clustering　methods.