diff --git a/docs/source/api/python/graph.rst b/docs/source/api/python/graph.rst
index 7fe28265b0b9..76ff4a81a779 100644
--- a/docs/source/api/python/graph.rst
+++ b/docs/source/api/python/graph.rst
@@ -55,6 +55,7 @@ Transforming graph
     DGLGraph.subgraphs
     DGLGraph.edge_subgraph
     DGLGraph.line_graph
+    DGLGraph.reverse
 
 Converting from/to other format
 -------------------------------
diff --git a/docs/source/api/python/index.rst b/docs/source/api/python/index.rst
index b357f4da460f..fafd708d8fe0 100644
--- a/docs/source/api/python/index.rst
+++ b/docs/source/api/python/index.rst
@@ -13,3 +13,4 @@ API Reference
    udf
    sampler
    data
+   transform
diff --git a/docs/source/api/python/transform.rst b/docs/source/api/python/transform.rst
new file mode 100644
index 000000000000..11dea2ddc829
--- /dev/null
+++ b/docs/source/api/python/transform.rst
@@ -0,0 +1,12 @@
+.. _apigraph:
+
+Transform -- Graph Transformation
+=================================
+
+.. automodule:: dgl.transform
+
+.. autosummary::
+    :toctree: ../../generated/
+
+    line_graph
+    reverse
diff --git a/docs/source/install/index.rst b/docs/source/install/index.rst
index f3eb13342c1e..173a5c4eb11d 100644
--- a/docs/source/install/index.rst
+++ b/docs/source/install/index.rst
@@ -59,7 +59,7 @@ The backend is controlled by ``DGLBACKEND`` environment variable, which defaults
 |         |         | `official website <https://pytorch.org>`_        |
 +---------+---------+--------------------------------------------------+
 | mxnet   | MXNet   | Requires nightly build; run the following        |
-|         |         | command to install (TODO):                       |
+|         |         | command to install:                              |
 |         |         |                                                  |
 |         |         | .. code:: bash                                   |
 |         |         |                                                  |
diff --git a/python/dgl/__init__.py b/python/dgl/__init__.py
index 1dec84b54da1..af6cd8b0799e 100644
--- a/python/dgl/__init__.py
+++ b/python/dgl/__init__.py
@@ -14,3 +14,4 @@
 from .traversal import *
 from .propagate import *
 from .udf import NodeBatch, EdgeBatch
+from .transform import *
diff --git a/python/dgl/graph.py b/python/dgl/graph.py
index 52152e25c377..008cff7cad18 100644
--- a/python/dgl/graph.py
+++ b/python/dgl/graph.py
@@ -3,6 +3,7 @@
 
 from collections import defaultdict
 
+import dgl
 from .base import ALL, is_all, DGLError
 from . import backend as F
 from . import init
@@ -2760,22 +2761,16 @@ def incidence_matrix(self, typestr, ctx=F.cpu()):
     def line_graph(self, backtracking=True, shared=False):
         """Return the line graph of this graph.
 
-        Parameters
-        ----------
-        backtracking : bool, optional
-            Whether the returned line graph is backtracking.
+        See :func:`~dgl.transform.line_graph`.
+        """
+        return dgl.line_graph(self, backtracking, shared)
 
-        shared : bool, optional
-            Whether the returned line graph shares representations with `self`.
+    def reverse(self, share_ndata=False, share_edata=False):
+        """Return the reverse of this graph.
 
-        Returns
-        -------
-        DGLGraph
-            The line graph of this graph.
+        See :func:`~dgl.transform.reverse`.
         """
-        graph_data = self._graph.line_graph(backtracking)
-        node_frame = self._edge_frame if shared else None
-        return DGLGraph(graph_data, node_frame)
+        return dgl.reverse(self, share_ndata, share_edata)
 
     def filter_nodes(self, predicate, nodes=ALL):
         """Return a tensor of node IDs that satisfy the given predicate.
diff --git a/python/dgl/transform.py b/python/dgl/transform.py
new file mode 100644
index 000000000000..5cfac8f1e0e1
--- /dev/null
+++ b/python/dgl/transform.py
@@ -0,0 +1,105 @@
+"""Module for graph transformation methods."""
+from .graph import DGLGraph
+from .batched_graph import BatchedDGLGraph
+
+__all__ = ['line_graph', 'reverse']
+
+
+def line_graph(g, backtracking=True, shared=False):
+    """Return the line graph of this graph.
+
+    Parameters
+    ----------
+    g : dgl.DGLGraph
+    backtracking : bool, optional
+        Whether the returned line graph is backtracking.
+    shared : bool, optional
+        Whether the returned line graph shares representations with `self`.
+
+    Returns
+    -------
+    DGLGraph
+        The line graph of this graph.
+    """
+    graph_data = g._graph.line_graph(backtracking)
+    node_frame = g._edge_frame if shared else None
+    return DGLGraph(graph_data, node_frame)
+
+def reverse(g, share_ndata=False, share_edata=False):
+    """Return the reverse of a graph
+
+    The reverse (also called converse, transpose) of a directed graph is another directed
+    graph on the same nodes with edges reversed in terms of direction.
+
+    Given a :class:`DGLGraph` object, we return another :class:`DGLGraph` object
+    representing its reverse.
+
+    Notes
+    -----
+    * This function does not support :class:`~dgl.BatchedDGLGraph` objects.
+    * We do not dynamically update the topology of a graph once that of its reverse changes.
+      This can be particularly problematic when the node/edge attrs are shared. For example,
+      if the topology of both the original graph and its reverse get changed independently,
+      you can get a mismatched node/edge feature.
+
+    Parameters
+    ----------
+    g : dgl.DGLGraph
+    share_ndata: bool, optional
+        If True, the original graph and the reversed graph share memory for node attributes.
+        Otherwise the reversed graph will not be initialized with node attributes.
+    share_edata: bool, optional
+        If True, the original graph and the reversed graph share memory for edge attributes.
+        Otherwise the reversed graph will not have edge attributes.
+
+    Examples
+    --------
+    Create a graph to reverse.
+
+    >>> import dgl
+    >>> import torch as th
+    >>> g = dgl.DGLGraph()
+    >>> g.add_nodes(3)
+    >>> g.add_edges([0, 1, 2], [1, 2, 0])
+    >>> g.ndata['h'] = th.tensor([[0.], [1.], [2.]])
+    >>> g.edata['h'] = th.tensor([[3.], [4.], [5.]])
+
+    Reverse the graph and examine its structure.
+
+    >>> rg = g.reverse(share_ndata=True, share_edata=True)
+    >>> print(rg)
+    DGLGraph with 3 nodes and 3 edges.
+    Node data: {'h': Scheme(shape=(1,), dtype=torch.float32)}
+    Edge data: {'h': Scheme(shape=(1,), dtype=torch.float32)}
+
+    The edges are reversed now.
+
+    >>> rg.has_edges_between([1, 2, 0], [0, 1, 2])
+    tensor([1, 1, 1])
+
+    Reversed edges have the same feature as the original ones.
+
+    >>> g.edges[[0, 2], [1, 0]].data['h'] == rg.edges[[1, 0], [0, 2]].data['h']
+    tensor([[1],
+            [1]], dtype=torch.uint8)
+
+    The node/edge features of the reversed graph share memory with the original
+    graph, which is helpful for both forward computation and back propagation.
+
+    >>> g.ndata['h'] = g.ndata['h'] + 1
+    >>> rg.ndata['h']
+    tensor([[1.],
+            [2.],
+            [3.]])
+    """
+    assert not isinstance(g, BatchedDGLGraph), \
+        'reverse is not supported for a BatchedDGLGraph object'
+    g_reversed = DGLGraph(multigraph=g.is_multigraph)
+    g_reversed.add_nodes(g.number_of_nodes())
+    g_edges = g.edges()
+    g_reversed.add_edges(g_edges[1], g_edges[0])
+    if share_ndata:
+        g_reversed._node_frame = g._node_frame
+    if share_edata:
+        g_reversed._edge_frame = g._edge_frame
+    return g_reversed
diff --git a/tests/pytorch/test_line_graph.py b/tests/pytorch/test_line_graph.py
deleted file mode 100644
index 0356ef92d670..000000000000
--- a/tests/pytorch/test_line_graph.py
+++ /dev/null
@@ -1,44 +0,0 @@
-import torch as th
-import networkx as nx
-import numpy as np
-import dgl
-import utils as U
-
-D = 5
-
-def test_line_graph():
-    N = 5
-    G = dgl.DGLGraph(nx.star_graph(N))
-    G.edata['h'] = th.randn((2 * N, D))
-    n_edges = G.number_of_edges()
-    L = G.line_graph(shared=True)
-    assert L.number_of_nodes() == 2 * N
-    L.ndata['h'] = th.randn((2 * N, D))
-    # update node features on line graph should reflect to edge features on
-    # original graph.
-    u = [0, 0, 2, 3]
-    v = [1, 2, 0, 0]
-    eid = G.edge_ids(u, v)
-    L.nodes[eid].data['h'] = th.zeros((4, D))
-    assert U.allclose(G.edges[u, v].data['h'], th.zeros((4, D)))
-
-    # adding a new node feature on line graph should also reflect to a new
-    # edge feature on original graph
-    data = th.randn(n_edges, D)
-    L.ndata['w'] = data
-    assert U.allclose(G.edata['w'], data)
-
-def test_no_backtracking():
-    N = 5
-    G = dgl.DGLGraph(nx.star_graph(N))
-    L = G.line_graph(backtracking=False)
-    assert L.number_of_nodes() == 2 * N
-    for i in range(1, N):
-        e1 = G.edge_id(0, i)
-        e2 = G.edge_id(i, 0)
-        assert not L.has_edge_between(e1, e2)
-        assert not L.has_edge_between(e2, e1)
-
-if __name__ == '__main__':
-    test_line_graph()
-    test_no_backtracking()
diff --git a/tests/pytorch/test_transform.py b/tests/pytorch/test_transform.py
new file mode 100644
index 000000000000..b57f6a05adb3
--- /dev/null
+++ b/tests/pytorch/test_transform.py
@@ -0,0 +1,101 @@
+import torch as th
+import networkx as nx
+import numpy as np
+import dgl
+import dgl.function as fn
+import utils as U
+
+D = 5
+
+# line graph related
+def test_line_graph():
+    N = 5
+    G = dgl.DGLGraph(nx.star_graph(N))
+    G.edata['h'] = th.randn((2 * N, D))
+    n_edges = G.number_of_edges()
+    L = G.line_graph(shared=True)
+    assert L.number_of_nodes() == 2 * N
+    L.ndata['h'] = th.randn((2 * N, D))
+    # update node features on line graph should reflect to edge features on
+    # original graph.
+    u = [0, 0, 2, 3]
+    v = [1, 2, 0, 0]
+    eid = G.edge_ids(u, v)
+    L.nodes[eid].data['h'] = th.zeros((4, D))
+    assert U.allclose(G.edges[u, v].data['h'], th.zeros((4, D)))
+
+    # adding a new node feature on line graph should also reflect to a new
+    # edge feature on original graph
+    data = th.randn(n_edges, D)
+    L.ndata['w'] = data
+    assert U.allclose(G.edata['w'], data)
+
+def test_no_backtracking():
+    N = 5
+    G = dgl.DGLGraph(nx.star_graph(N))
+    L = G.line_graph(backtracking=False)
+    assert L.number_of_nodes() == 2 * N
+    for i in range(1, N):
+        e1 = G.edge_id(0, i)
+        e2 = G.edge_id(i, 0)
+        assert not L.has_edge_between(e1, e2)
+        assert not L.has_edge_between(e2, e1)
+
+# reverse graph related
+def test_reverse():
+    g = dgl.DGLGraph()
+    g.add_nodes(5)
+    # The graph need not to be completely connected.
+    g.add_edges([0, 1, 2], [1, 2, 1])
+    g.ndata['h'] = th.tensor([[0.], [1.], [2.], [3.], [4.]])
+    g.edata['h'] = th.tensor([[5.], [6.], [7.]])
+    rg = g.reverse()
+
+    assert g.is_multigraph == rg.is_multigraph
+
+    assert g.number_of_nodes() == rg.number_of_nodes()
+    assert g.number_of_edges() == rg.number_of_edges()
+    assert U.allclose(rg.has_edges_between([1, 2, 1], [0, 1, 2]).float(), th.ones(3))
+    assert g.edge_id(0, 1) == rg.edge_id(1, 0)
+    assert g.edge_id(1, 2) == rg.edge_id(2, 1)
+    assert g.edge_id(2, 1) == rg.edge_id(1, 2)
+
+def test_reverse_shared_frames():
+    g = dgl.DGLGraph()
+    g.add_nodes(3)
+    g.add_edges([0, 1, 2], [1, 2, 1])
+    g.ndata['h'] = th.tensor([[0.], [1.], [2.]], requires_grad=True)
+    g.edata['h'] = th.tensor([[3.], [4.], [5.]], requires_grad=True)
+
+    rg = g.reverse(share_ndata=True, share_edata=True)
+    assert U.allclose(g.ndata['h'], rg.ndata['h'])
+    assert U.allclose(g.edata['h'], rg.edata['h'])
+    assert U.allclose(g.edges[[0, 2], [1, 1]].data['h'],
+                      rg.edges[[1, 1], [0, 2]].data['h'])
+
+    rg.ndata['h'] = rg.ndata['h'] + 1
+    assert U.allclose(rg.ndata['h'], g.ndata['h'])
+
+    g.edata['h'] = g.edata['h'] - 1
+    assert U.allclose(rg.edata['h'], g.edata['h'])
+
+    src_msg = fn.copy_src(src='h', out='m')
+    sum_reduce = fn.sum(msg='m', out='h')
+
+    rg.update_all(src_msg, sum_reduce)
+    assert U.allclose(g.ndata['h'], rg.ndata['h'])
+
+    # Grad check
+    g.ndata['h'].retain_grad()
+    rg.ndata['h'].retain_grad()
+    loss_func = th.nn.MSELoss()
+    target = th.zeros(3, 1)
+    loss = loss_func(rg.ndata['h'], target)
+    loss.backward()
+    assert U.allclose(g.ndata['h'].grad, rg.ndata['h'].grad)
+
+if __name__ == '__main__':
+    test_line_graph()
+    test_no_backtracking()
+    test_reverse()
+    test_reverse_shared_frames()