Detecting　clusters　over　attributed　graphs　is　a　fundamental　task　in　the　graph　analysis　field.　The　goal　is　to　partition　nodes　into　dense　clusters　based　on　both　their　attributes　and　structures.　Modern　graph　neural　networks　provide　facilitation　to　jointly　capture　the　above　information　in　attributed　graphs　with　a　feature　aggregation　manner,　and　have　achieved　great　success　in　attributed　graph　clustering.　However,　existing　methods　mainly　focus　on　capturing　the　proximity　information　in　graphs　and　often　fail　to　learn　cluster-friendly　features　during　the　training　of　models.　Besides,　similar　to　many　deep　clustering　frameworks,　current　methods　based　on　graph　neural　networks　require　a　preassigned　cluster　number　before　estimating　the　clusters.　To　address　these　limitations,　we　propose　in　this　paper　a　deep　attributed　clustering　method　based　on　self-separated　graph　neural　networks　and　parameter-free　cluster　estimation.　First,　to　learn　cluster-friendly　features,　we　jointly　optimize　a　jumping　graph　convolutional　auto-encoder　with　a　self-separation　regularizer,　which　learns　clusters　with　changing　sizes　while　keeping　dense　intra-cluster　structures　and　sparse　inter　structures.　Second,　an　additional　softmax　auto-encoder　is　trained　to　determine　the　natural　cluster　number　from　the　data.　The　hidden　units　capture　cluster　structures　and　can　be　used　to　estimate　the　number　of　clusters.　Extensive　experiments　show　the　effectiveness　of　the　proposed　model.　(C)　2021　Elsevier　Ltd.　All　rights　reserved.