The　graph　convolutional　network　(GCN)-based　clustering　approaches　have　achieved　the　impressive　performance　due　to　strong　ability　of　exploiting　the　topological　structure.　The　adjacency　graph　seriously　affects　the　clustering　performance,　especially　for　non-graph　data.　Existing　approaches　usually　conduct　two　independent　steps,　i.e.,　constructing　a　fixed　graph　structure　and　then　graph　embedding　representation　learning　by　GCN.　However,　the　constructed　graph　structure　may　be　unreliable　one　due　to　noisy　data,　resulting　in　sub-optimal　graph　embedding　representation.　In　this　paper,　we　propose　an　adaptive　graph　convolutional　clustering　network　(AGCCN)　to　alternatively　learn　the　similarity　graph　structure　and　node　embedding　representation　in　a　unified　framework.　Our　AGCCN　learns　the　weighted　adjacency　graph　adaptively　from　the　node　representations　by　solving　the　optimization　problem　of　graph　learning,　in　which　adaptive　and　optimal　neighbors　for　each　sample　are　assigned　with　probabilistic　way　according　to　local　connectivity.　Then,　the　attribute　feature　extracted　by　parallel　Auto-Encoder　(AE)　module　is　fused　into　the　input　of　adaptive　graph　convolution　module　layer-by-layer　to　learn　the　comprehensive　node　embedding　representation　and　strengthen　its　representation　ability.　This　also　skillfully　alleviates　the　over-smoothing　problem　of　GCN.　To　further　improve　the　discriminant　ability　of　node　representation,　a　dual　self-supervised　clustering　mechanism　is　designed　to　guide　model　optimization　with　pseudo-labels　information.　Extensive　experimental　results　on　various　real-world　datasets　consistently　show　the　superiority　and　effectiveness　of　the　proposed　deep　graph　clustering　method.(c)　2022　Elsevier　Ltd.　All　rights　reserved.