diff --git a/src/operator/contrib/dgl_graph.cc b/src/operator/contrib/dgl_graph.cc
index 2925a86a127f..98597bd473dc 100644
--- a/src/operator/contrib/dgl_graph.cc
+++ b/src/operator/contrib/dgl_graph.cc
@@ -1393,5 +1393,196 @@ Example::
 .set_attr<FComputeEx>("FComputeEx<cpu>", DGLAdjacencyForwardEx<cpu>)
 .add_argument("data", "NDArray-or-Symbol", "Input ndarray");
 
+///////////////////////// Compact subgraphs ///////////////////////////
+
+struct SubgraphCompactParam : public dmlc::Parameter<SubgraphCompactParam> {
+  int num_args;
+  bool return_mapping;
+  nnvm::Tuple<nnvm::dim_t> graph_sizes;
+  DMLC_DECLARE_PARAMETER(SubgraphCompactParam) {
+    DMLC_DECLARE_FIELD(num_args).set_lower_bound(2)
+    .describe("Number of input arguments.");
+    DMLC_DECLARE_FIELD(return_mapping)
+    .describe("Return mapping of vid and eid between the subgraph and the parent graph.");
+    DMLC_DECLARE_FIELD(graph_sizes)
+    .describe("the number of vertices in each graph.");
+  }
+};  // struct SubgraphCompactParam
+
+DMLC_REGISTER_PARAMETER(SubgraphCompactParam);
+
+static inline size_t get_num_graphs(const SubgraphCompactParam &params) {
+  // Each CSR needs a 1D array to store the original vertex Id for each row.
+  return params.num_args / 2;
+}
+
+static void CompactSubgraph(const NDArray &csr, const NDArray &vids,
+                            const NDArray &out_csr, size_t graph_size) {
+  TBlob in_idx_data = csr.aux_data(csr::kIdx);
+  TBlob in_ptr_data = csr.aux_data(csr::kIndPtr);
+  const dgl_id_t *indices_in = in_idx_data.dptr<dgl_id_t>();
+  const dgl_id_t *indptr_in = in_ptr_data.dptr<dgl_id_t>();
+  const dgl_id_t *row_ids = vids.data().dptr<dgl_id_t>();
+  size_t num_elems = csr.aux_data(csr::kIdx).shape_.Size();
+  // The last element in vids is the actual number of vertices in the subgraph.
+  CHECK_EQ(vids.shape()[0], in_ptr_data.shape_[0]);
+  CHECK_EQ((size_t) row_ids[vids.shape()[0] - 1], graph_size);
+
+  // Prepare the Id map from the original graph to the subgraph.
+  std::unordered_map<dgl_id_t, dgl_id_t> id_map;
+  id_map.reserve(graph_size);
+  for (size_t i = 0; i < graph_size; i++) {
+    id_map.insert(std::pair<dgl_id_t, dgl_id_t>(row_ids[i], i));
+    CHECK_NE(row_ids[i], -1);
+  }
+
+  TShape nz_shape(1);
+  nz_shape[0] = num_elems;
+  TShape indptr_shape(1);
+  CHECK_EQ(out_csr.shape()[0], graph_size);
+  indptr_shape[0] = graph_size + 1;
+  CHECK_GE(in_ptr_data.shape_[0], indptr_shape[0]);
+
+  out_csr.CheckAndAllocData(nz_shape);
+  out_csr.CheckAndAllocAuxData(csr::kIdx, nz_shape);
+  out_csr.CheckAndAllocAuxData(csr::kIndPtr, indptr_shape);
+
+  dgl_id_t *indices_out = out_csr.aux_data(csr::kIdx).dptr<dgl_id_t>();
+  dgl_id_t *indptr_out = out_csr.aux_data(csr::kIndPtr).dptr<dgl_id_t>();
+  dgl_id_t *sub_eids = out_csr.data().dptr<dgl_id_t>();
+  std::copy(indptr_in, indptr_in + indptr_shape[0], indptr_out);
+  for (int64_t i = 0; i < nz_shape[0]; i++) {
+    dgl_id_t old_id = indices_in[i];
+    auto it = id_map.find(old_id);
+    CHECK(it != id_map.end());
+    indices_out[i] = it->second;
+    sub_eids[i] = i;
+  }
+}
+
+static void SubgraphCompactComputeExCPU(const nnvm::NodeAttrs& attrs,
+                                        const OpContext& ctx,
+                                        const std::vector<NDArray>& inputs,
+                                        const std::vector<OpReqType>& req,
+                                        const std::vector<NDArray>& outputs) {
+  const SubgraphCompactParam& params = nnvm::get<SubgraphCompactParam>(attrs.parsed);
+  int num_g = get_num_graphs(params);
+#pragma omp parallel for
+  for (int i = 0; i < num_g; i++) {
+    CompactSubgraph(inputs[i], inputs[i + num_g], outputs[i], params.graph_sizes[i]);
+  }
+}
+
+static bool SubgraphCompactStorageType(const nnvm::NodeAttrs& attrs,
+                                       const int dev_mask,
+                                       DispatchMode* dispatch_mode,
+                                       std::vector<int> *in_attrs,
+                                       std::vector<int> *out_attrs) {
+  const SubgraphCompactParam& params = nnvm::get<SubgraphCompactParam>(attrs.parsed);
+  size_t num_g = get_num_graphs(params);
+  CHECK_EQ(num_g * 2, in_attrs->size());
+  // These are the input subgraphs.
+  for (size_t i = 0; i < num_g; i++)
+    CHECK_EQ(in_attrs->at(i), kCSRStorage);
+  // These are the vertex Ids in the original graph.
+  for (size_t i = 0; i < num_g; i++)
+    CHECK_EQ(in_attrs->at(i + num_g), kDefaultStorage);
+
+  bool success = true;
+  *dispatch_mode = DispatchMode::kFComputeEx;
+  for (size_t i = 0; i < out_attrs->size(); i++) {
+    if (!type_assign(&(*out_attrs)[i], mxnet::kCSRStorage))
+      success = false;
+  }
+  return success;
+}
+
+static bool SubgraphCompactShape(const nnvm::NodeAttrs& attrs,
+                                 std::vector<TShape> *in_attrs,
+                                 std::vector<TShape> *out_attrs) {
+  const SubgraphCompactParam& params = nnvm::get<SubgraphCompactParam>(attrs.parsed);
+  size_t num_g = get_num_graphs(params);
+  CHECK_EQ(num_g * 2, in_attrs->size());
+  // These are the input subgraphs.
+  for (size_t i = 0; i < num_g; i++) {
+    CHECK_EQ(in_attrs->at(i).ndim(), 2U);
+    CHECK_GE(in_attrs->at(i)[0], params.graph_sizes[i]);
+    CHECK_GE(in_attrs->at(i)[1], params.graph_sizes[i]);
+  }
+  // These are the vertex Ids in the original graph.
+  for (size_t i = 0; i < num_g; i++) {
+    CHECK_EQ(in_attrs->at(i + num_g).ndim(), 1U);
+    CHECK_GE(in_attrs->at(i + num_g)[0], params.graph_sizes[i]);
+  }
+
+  for (size_t i = 0; i < num_g; i++) {
+    TShape gshape(2);
+    gshape[0] = params.graph_sizes[i];
+    gshape[1] = params.graph_sizes[i];
+    out_attrs->at(i) = gshape;
+    if (params.return_mapping)
+      out_attrs->at(i + num_g) = gshape;
+  }
+  return true;
+}
+
+static bool SubgraphCompactType(const nnvm::NodeAttrs& attrs,
+                                std::vector<int> *in_attrs,
+                                std::vector<int> *out_attrs) {
+  for (size_t i = 0; i < in_attrs->size(); i++) {
+    CHECK_EQ(in_attrs->at(i), mshadow::kInt64);
+  }
+  for (size_t i = 0; i < out_attrs->size(); i++) {
+    out_attrs->at(i) = mshadow::kInt64;
+  }
+  return true;
+}
+
+NNVM_REGISTER_OP(_contrib_dgl_graph_compact)
+.describe(R"code(This operator compacts a CSR matrix generated by
+csr_neighbor_uniform_sample and csr_neighbor_non_uniform_sample.
+The CSR matrices generated by these two operators may have many empty
+rows at the end. This operator removes these empty rows and empty columns.
+Example::
+  subgs = mx.nd.contrib.csr_neighbor_uniform_sample(csr, seed, num_hops=1,
+          num_neighbor=2, max_num_vertices=5)
+  subg_v = subgs[0]
+  subg = subgs[1]
+  compacts = mx.nd.contrib.dgl_graph_compact(subg, subg_v,
+          graph_sizes=(subg_v[-1].asnumpy()[0]))
+)code" ADD_FILELINE)
+.set_attr_parser(ParamParser<SubgraphCompactParam>)
+.set_num_inputs([](const NodeAttrs& attrs) {
+  const SubgraphCompactParam& params = nnvm::get<SubgraphCompactParam>(attrs.parsed);
+  return params.num_args;
+})
+.set_num_outputs([](const NodeAttrs& attrs) {
+  const SubgraphCompactParam& params = nnvm::get<SubgraphCompactParam>(attrs.parsed);
+  int num_varray = get_num_graphs(params);
+  if (params.return_mapping)
+    return num_varray * 2;
+  else
+    return num_varray;
+})
+.set_attr<nnvm::FListInputNames>("FListInputNames",
+    [](const NodeAttrs& attrs) {
+  const SubgraphCompactParam& params = nnvm::get<SubgraphCompactParam>(attrs.parsed);
+  std::vector<std::string> names;
+  names.reserve(params.num_args);
+  size_t num_graphs = get_num_graphs(params);
+  for (size_t i = 0; i < num_graphs; i++)
+    names.push_back("graph" + std::to_string(i));
+  for (size_t i = 0; i < num_graphs; ++i)
+    names.push_back("varray" + std::to_string(i));
+  return names;
+})
+.set_attr<FInferStorageType>("FInferStorageType", SubgraphCompactStorageType)
+.set_attr<nnvm::FInferShape>("FInferShape", SubgraphCompactShape)
+.set_attr<nnvm::FInferType>("FInferType", SubgraphCompactType)
+.set_attr<FComputeEx>("FComputeEx<cpu>", SubgraphCompactComputeExCPU)
+.set_attr<std::string>("key_var_num_args", "num_args")
+.add_argument("graph_data", "NDArray-or-Symbol[]", "Input graphs and input vertex Ids.")
+.add_arguments(SubgraphCompactParam::__FIELDS__());
+
 }  // namespace op
 }  // namespace mxnet