def batch(graphs, ndata=ALL, edata=ALL):
    r"""Batch a collection of :class:`DGLGraph` s into one graph for more efficient
    graph computation.

    Each input graph becomes one disjoint component of the batched graph. The nodes
    and edges are relabeled to be disjoint segments:

    =================  =========  =================  ===  =========
                       graphs[0]  graphs[1]          ...  graphs[k]
    =================  =========  =================  ===  =========
    Original node ID   0 ~ N_0    0 ~ N_1            ...  0 ~ N_k
    New node ID        0 ~ N_0    N_0 ~ N_0+N_1      ...  \sum_{i=0}^{k-1} N_i ~
                                                          \sum_{i=0}^k N_i
    =================  =========  =================  ===  =========

    Because of this, many of the computations on a batched graph are the same as if
    performed on each graph individually, but become much more efficient
    since they can be parallelized easily. This makes ``dgl.batch`` very useful
    for tasks dealing with many graph samples such as graph classification tasks.

    For heterograph inputs, they must share the same set of relations (i.e., node types
    and edge types) and the function will perform batching on each relation one by one.
    Thus, the result is also a heterograph and has the same set of relations as the inputs.

    The numbers of nodes and edges of the input graphs are accessible via the
    :func:`DGLGraph.batch_num_nodes` and :func:`DGLGraph.batch_num_edges` attributes
    of the resulting graph. For homogeneous graphs, they are 1D integer tensors,
    with each element being the number of nodes/edges of the corresponding input graph. For
    heterographs, they are dictionaries of 1D integer tensors, with node
    type or edge type as the keys.

    The function supports batching batched graphs. The batch size of the result
    graph is the sum of the batch sizes of all the input graphs.

    By default, node/edge features are batched by concatenating the feature tensors
    of all input graphs. This thus requires features of the same name to have
    the same data type and feature size. One can pass ``None`` to the ``ndata``
    or ``edata`` argument to prevent feature batching, or pass a list of strings
    to specify which features to batch.

    To unbatch the graph back to a list, use the :func:`dgl.unbatch` function.

    Parameters
    ----------
    graphs : list[DGLGraph]
        Input graphs.
    ndata : list[str], None, optional
        Node features to batch.
    edata : list[str], None, optional
        Edge features to batch.

    Returns
    -------
    DGLGraph
        Batched graph.

    Examples
    --------

    Batch homogeneous graphs

    >>> import dgl
    >>> import torch as th
    >>> # 4 nodes, 3 edges
    >>> g1 = dgl.graph((th.tensor([0, 1, 2]), th.tensor([1, 2, 3])))
    >>> # 3 nodes, 4 edges
    >>> g2 = dgl.graph((th.tensor([0, 0, 0, 1]), th.tensor([0, 1, 2, 0])))
    >>> bg = dgl.batch([g1, g2])
    >>> bg
    Graph(num_nodes=7, num_edges=7,
          ndata_schemes={}
          edata_schemes={})
    >>> bg.batch_size
    2
    >>> bg.batch_num_nodes()
    tensor([4, 3])
    >>> bg.batch_num_edges()
    tensor([3, 4])
    >>> bg.edges()
    (tensor([0, 1, 2, 4, 4, 4, 5], tensor([1, 2, 3, 4, 5, 6, 4]))

    Batch batched graphs

    >>> bbg = dgl.batch([bg, bg])
    >>> bbg.batch_size
    4
    >>> bbg.batch_num_nodes()
    tensor([4, 3, 4, 3])
    >>> bbg.batch_num_edges()
    tensor([3, 4, 3, 4])

    Batch graphs with feature data

    >>> g1.ndata['x'] = th.zeros(g1.num_nodes(), 3)
    >>> g1.edata['w'] = th.ones(g1.num_edges(), 2)
    >>> g2.ndata['x'] = th.ones(g2.num_nodes(), 3)
    >>> g2.edata['w'] = th.zeros(g2.num_edges(), 2)
    >>> bg = dgl.batch([g1, g2])
    >>> bg.ndata['x']
    tensor([[0, 0, 0],
            [0, 0, 0],
            [0, 0, 0],
            [0, 0, 0],
            [1, 1, 1],
            [1, 1, 1],
            [1, 1, 1]])
    >>> bg.edata['w']
    tensor([[1, 1],
            [1, 1],
            [1, 1],
            [0, 0],
            [0, 0],
            [0, 0],
            [0, 0]])

    Batch heterographs

    >>> hg1 = dgl.heterograph({
    ...     ('user', 'plays', 'game') : (th.tensor([0, 1]), th.tensor([0, 0]))})
    >>> hg2 = dgl.heterograph({
    ...     ('user', 'plays', 'game') : (th.tensor([0, 0, 0]), th.tensor([1, 0, 2]))})
    >>> bhg = dgl.batch([hg1, hg2])
    >>> bhg
    Graph(num_nodes={'user': 3, 'game': 4},
          num_edges={('user', 'plays', 'game'): 5},
          metagraph=[('drug', 'game')])
    >>> bhg.batch_size
    2
    >>> bhg.batch_num_nodes()
    {'user' : tensor([2, 1]), 'game' : tensor([1, 3])}
    >>> bhg.batch_num_edges()
    {('user', 'plays', 'game') : tensor([2, 3])}

    See Also
    --------
    unbatch
    """
    if len(graphs) == 0:
        raise DGLError("The input list of graphs cannot be empty.")
    if not (is_all(ndata) or isinstance(ndata, list) or ndata is None):
        raise DGLError(
            "Invalid argument ndata: must be a string list but got {}.".format(
                type(ndata)
            )
        )
    if not (is_all(edata) or isinstance(edata, list) or edata is None):
        raise DGLError(
            "Invalid argument edata: must be a string list but got {}.".format(
                type(edata)
            )
        )
    if any(g.is_block for g in graphs):
        raise DGLError("Batching a MFG is not supported.")

    relations = list(graphs[0].canonical_etypes)
    relation_ids = [graphs[0].get_etype_id(r) for r in relations]
    ntypes = list(graphs[0].ntypes)
    ntype_ids = [graphs[0].get_ntype_id(n) for n in ntypes]
    etypes = [etype for _, etype, _ in relations]

    gidx = disjoint_union(
        graphs[0]._graph.metagraph, [g._graph for g in graphs]
    )
    retg = DGLGraph(gidx, ntypes, etypes)

    # Compute batch num nodes
    bnn = {}
    for ntype in ntypes:
        bnn[ntype] = F.cat([g.batch_num_nodes(ntype) for g in graphs], 0)
    retg.set_batch_num_nodes(bnn)

    # Compute batch num edges
    bne = {}
    for etype in relations:
        bne[etype] = F.cat([g.batch_num_edges(etype) for g in graphs], 0)
    retg.set_batch_num_edges(bne)

    # Batch node feature
    if ndata is not None:
        for ntype_id, ntype in zip(ntype_ids, ntypes):
            all_empty = all(g._graph.num_nodes(ntype_id) == 0 for g in graphs)
            frames = [
                g._node_frames[ntype_id]
                for g in graphs
                if g._graph.num_nodes(ntype_id) > 0 or all_empty
            ]
            # TODO: do we require graphs with no nodes/edges to have the same schema?  Currently
            # we allow empty graphs to have no features during batching.
            ret_feat = _batch_feat_dicts(
                frames, ndata, 'nodes["{}"].data'.format(ntype)
            )
            retg.nodes[ntype].data.update(ret_feat)

    # Batch edge feature
    if edata is not None:
        for etype_id, etype in zip(relation_ids, relations):
            all_empty = all(g._graph.num_edges(etype_id) == 0 for g in graphs)
            frames = [
                g._edge_frames[etype_id]
                for g in graphs
                if g._graph.num_edges(etype_id) > 0 or all_empty
            ]
            # TODO: do we require graphs with no nodes/edges to have the same schema?  Currently
            # we allow empty graphs to have no features during batching.
            ret_feat = _batch_feat_dicts(
                frames, edata, "edges[{}].data".format(etype)
            )
            retg.edges[etype].data.update(ret_feat)

    return retg
Batch a collection of :class:`DGLGraph` s into one graph for more efficient
    graph computation.

    Each input graph becomes one disjoint component of the batched graph. The nodes
    and edges are relabeled to be disjoint segments:

    =================  =========  =================  ===  =========
                       graphs[0]  graphs[1]          ...  graphs[k]
    =================  =========  =================  ===  =========
    Original node ID   0 ~ N_0    0 ~ N_1            ...  0 ~ N_k
    New node ID        0 ~ N_0    N_0 ~ N_0+N_1      ...  \sum_{i=0}^{k-1} N_i ~
                                                          \sum_{i=0}^k N_i
    =================  =========  =================  ===  =========

    Because of this, many of the computations on a batched graph are the same as if
    performed on each graph individually, but become much more efficient
    since they can be parallelized easily. This makes ``dgl.batch`` very useful
    for tasks dealing with many graph samples such as graph classification tasks.

    For heterograph inputs, they must share the same set of relations (i.e., node types
    and edge types) and the function will perform batching on each relation one by one.
    Thus, the result is also a heterograph and has the same set of relations as the inputs.

    The numbers of nodes and edges of the input graphs are accessible via the
    :func:`DGLGraph.batch_num_nodes` and :func:`DGLGraph.batch_num_edges` attributes
    of the resulting graph. For homogeneous graphs, they are 1D integer tensors,
    with each element being the number of nodes/edges of the corresponding input graph. For
    heterographs, they are dictionaries of 1D integer tensors, with node
    type or edge type as the keys.

    The function supports batching batched graphs. The batch size of the result
    graph is the sum of the batch sizes of all the input graphs.

    By default, node/edge features are batched by concatenating the feature tensors
    of all input graphs. This thus requires features of the same name to have
    the same data type and feature size. One can pass ``None`` to the ``ndata``
    or ``edata`` argument to prevent feature batching, or pass a list of strings
    to specify which features to batch.

    To unbatch the graph back to a list, use the :func:`dgl.unbatch` function.

    Parameters
    ----------
    graphs : list[DGLGraph]
        Input graphs.
    ndata : list[str], None, optional
        Node features to batch.
    edata : list[str], None, optional
        Edge features to batch.

    Returns
    -------
    DGLGraph
        Batched graph.

    Examples
    --------

    Batch homogeneous graphs

    >>> import dgl
    >>> import torch as th
    >>> # 4 nodes, 3 edges
    >>> g1 = dgl.graph((th.tensor([0, 1, 2]), th.tensor([1, 2, 3])))
    >>> # 3 nodes, 4 edges
    >>> g2 = dgl.graph((th.tensor([0, 0, 0, 1]), th.tensor([0, 1, 2, 0])))
    >>> bg = dgl.batch([g1, g2])
    >>> bg
    Graph(num_nodes=7, num_edges=7,
          ndata_schemes={}
          edata_schemes={})
    >>> bg.batch_size
    2
    >>> bg.batch_num_nodes()
    tensor([4, 3])
    >>> bg.batch_num_edges()
    tensor([3, 4])
    >>> bg.edges()
    (tensor([0, 1, 2, 4, 4, 4, 5], tensor([1, 2, 3, 4, 5, 6, 4]))

    Batch batched graphs

    >>> bbg = dgl.batch([bg, bg])
    >>> bbg.batch_size
    4
    >>> bbg.batch_num_nodes()
    tensor([4, 3, 4, 3])
    >>> bbg.batch_num_edges()
    tensor([3, 4, 3, 4])

    Batch graphs with feature data

    >>> g1.ndata['x'] = th.zeros(g1.num_nodes(), 3)
    >>> g1.edata['w'] = th.ones(g1.num_edges(), 2)
    >>> g2.ndata['x'] = th.ones(g2.num_nodes(), 3)
    >>> g2.edata['w'] = th.zeros(g2.num_edges(), 2)
    >>> bg = dgl.batch([g1, g2])
    >>> bg.ndata['x']
    tensor([[0, 0, 0],
            [0, 0, 0],
            [0, 0, 0],
            [0, 0, 0],
            [1, 1, 1],
            [1, 1, 1],
            [1, 1, 1]])
    >>> bg.edata['w']
    tensor([[1, 1],
            [1, 1],
            [1, 1],
            [0, 0],
            [0, 0],
            [0, 0],
            [0, 0]])

    Batch heterographs

    >>> hg1 = dgl.heterograph({
    ...     ('user', 'plays', 'game') : (th.tensor([0, 1]), th.tensor([0, 0]))})
    >>> hg2 = dgl.heterograph({
    ...     ('user', 'plays', 'game') : (th.tensor([0, 0, 0]), th.tensor([1, 0, 2]))})
    >>> bhg = dgl.batch([hg1, hg2])
    >>> bhg
    Graph(num_nodes={'user': 3, 'game': 4},
          num_edges={('user', 'plays', 'game'): 5},
          metagraph=[('drug', 'game')])
    >>> bhg.batch_size
    2
    >>> bhg.batch_num_nodes()
    {'user' : tensor([2, 1]), 'game' : tensor([1, 3])}
    >>> bhg.batch_num_edges()
    {('user', 'plays', 'game') : tensor([2, 3])}

    See Also
    --------
    unbatch
    
python/dgl/batch.py