"""Classes and functions for batching multiple graphs together."""
from __future__ import absolute_import
from collections.abc import Iterable
import numpy as np
from .base import ALL, is_all, DGLError
from .frame import FrameRef, Frame
from .graph import DGLGraph
from . import graph_index as gi
from . import backend as F
from . import utils
__all__ = ['BatchedDGLGraph', 'batch', 'unbatch', 'split',
'sum_nodes', 'sum_edges', 'mean_nodes', 'mean_edges',
'max_nodes', 'max_edges']
[docs]class BatchedDGLGraph(DGLGraph):
"""Class for batched DGL graphs.
A :class:`BatchedDGLGraph` basically merges a list of small graphs into a giant
graph so that one can perform message passing and readout over a batch of graphs
simultaneously.
The nodes and edges are re-indexed with a new id in the batched graph with the
rule below:
====== ========== ======================== === ==========================
item Graph 1 Graph 2 ... Graph k
====== ========== ======================== === ==========================
raw id 0, ..., N1 0, ..., N2 ... ..., Nk
new id 0, ..., N1 N1 + 1, ..., N1 + N2 + 1 ... ..., N1 + ... + Nk + k - 1
====== ========== ======================== === ==========================
The batched graph is read-only, i.e. one cannot further add nodes and edges.
A ``RuntimeError`` will be raised if one attempts.
To modify the features in :class:`BatchedDGLGraph` has no effect on the original
graphs. See the examples below about how to work around.
Parameters
----------
graph_list : iterable
A collection of :class:`~dgl.DGLGraph` objects to be batched.
node_attrs : None, str or iterable, optional
The node attributes to be batched. If ``None``, the :class:`BatchedDGLGraph` object
will not have any node attributes. By default, all node attributes will be batched.
An error will be raised if graphs having nodes have different attributes. If ``str``
or ``iterable``, this should specify exactly what node attributes to be batched.
edge_attrs : None, str or iterable, optional
Same as for the case of :attr:`node_attrs`
Examples
--------
Create two :class:`~dgl.DGLGraph` objects.
**Instantiation:**
>>> import dgl
>>> import torch as th
>>> g1 = dgl.DGLGraph()
>>> g1.add_nodes(2) # Add 2 nodes
>>> g1.add_edge(0, 1) # Add edge 0 -> 1
>>> g1.ndata['hv'] = th.tensor([[0.], [1.]]) # Initialize node features
>>> g1.edata['he'] = th.tensor([[0.]]) # Initialize edge features
>>> g2 = dgl.DGLGraph()
>>> g2.add_nodes(3) # Add 3 nodes
>>> g2.add_edges([0, 2], [1, 1]) # Add edges 0 -> 1, 2 -> 1
>>> g2.ndata['hv'] = th.tensor([[2.], [3.], [4.]]) # Initialize node features
>>> g2.edata['he'] = th.tensor([[1.], [2.]]) # Initialize edge features
Merge two :class:`~dgl.DGLGraph` objects into one :class:`BatchedDGLGraph` object.
When merging a list of graphs, we can choose to include only a subset of the attributes.
>>> bg = dgl.batch([g1, g2], edge_attrs=None)
>>> bg.edata
{}
Below one can see that the nodes are re-indexed. The edges are re-indexed in
the same way.
>>> bg.nodes()
tensor([0, 1, 2, 3, 4])
>>> bg.ndata['hv']
tensor([[0.],
[1.],
[2.],
[3.],
[4.]])
**Property:**
We can still get a brief summary of the graphs that constitute the batched graph.
>>> bg.batch_size
2
>>> bg.batch_num_nodes
[2, 3]
>>> bg.batch_num_edges
[1, 2]
**Readout:**
Another common demand for graph neural networks is graph readout, which is a
function that takes in the node attributes and/or edge attributes for a graph
and outputs a vector summarizing the information in the graph.
:class:`BatchedDGLGraph` also supports performing readout for a batch of graphs at once.
Below we take the built-in readout function :func:`sum_nodes` as an example, which
sums over a particular kind of node attribute for each graph.
>>> dgl.sum_nodes(bg, 'hv') # Sum the node attribute 'hv' for each graph.
tensor([[1.], # 0 + 1
[9.]]) # 2 + 3 + 4
**Message passing:**
For message passing and related operations, :class:`BatchedDGLGraph` acts exactly
the same as :class:`~dgl.DGLGraph`.
**Update Attributes:**
Updating the attributes of the batched graph has no effect on the original graphs.
>>> bg.edata['he'] = th.zeros(3, 2)
>>> g2.edata['he']
tensor([[1.],
[2.]])}
Instead, we can decompose the batched graph back into a list of graphs and use them
to replace the original graphs.
>>> g1, g2 = dgl.unbatch(bg) # returns a list of DGLGraph objects
>>> g2.edata['he']
tensor([[0., 0.],
[0., 0.]])}
"""
def __init__(self, graph_list, node_attrs, edge_attrs):
def _get_num_item_and_attr_types(g, mode):
if mode == 'node':
num_items = g.number_of_nodes()
attr_types = set(g.node_attr_schemes().keys())
elif mode == 'edge':
num_items = g.number_of_edges()
attr_types = set(g.edge_attr_schemes().keys())
return num_items, attr_types
def _init_attrs(attrs, mode):
if attrs is None:
return []
elif is_all(attrs):
attrs = set()
# Check if at least a graph has mode items and associated features.
for i, g in enumerate(graph_list):
g_num_items, g_attrs = _get_num_item_and_attr_types(g, mode)
if g_num_items > 0 and len(g_attrs) > 0:
attrs = g_attrs
ref_g_index = i
break
# Check if all the graphs with mode items have the same associated features.
if len(attrs) > 0:
for i, g in enumerate(graph_list):
g = graph_list[i]
g_num_items, g_attrs = _get_num_item_and_attr_types(g, mode)
if g_attrs != attrs and g_num_items > 0:
raise ValueError('Expect graph {0} and {1} to have the same {2} '
'attributes when {2}_attrs=ALL, got {3} and {4}.'
.format(ref_g_index, i, mode, attrs, g_attrs))
return attrs
elif isinstance(attrs, str):
return [attrs]
elif isinstance(attrs, Iterable):
return attrs
else:
raise ValueError('Expected {} attrs to be of type None str or Iterable, '
'got type {}'.format(mode, type(attrs)))
node_attrs = _init_attrs(node_attrs, 'node')
edge_attrs = _init_attrs(edge_attrs, 'edge')
# create batched graph index
batched_index = gi.disjoint_union([g._graph for g in graph_list])
# create batched node and edge frames
if len(node_attrs) == 0:
batched_node_frame = FrameRef(Frame(num_rows=batched_index.number_of_nodes()))
else:
# NOTE: following code will materialize the columns of the input graphs.
cols = {key: F.cat([gr._node_frame[key] for gr in graph_list
if gr.number_of_nodes() > 0], dim=0)
for key in node_attrs}
batched_node_frame = FrameRef(Frame(cols))
if len(edge_attrs) == 0:
batched_edge_frame = FrameRef(Frame(num_rows=batched_index.number_of_edges()))
else:
cols = {key: F.cat([gr._edge_frame[key] for gr in graph_list
if gr.number_of_edges() > 0], dim=0)
for key in edge_attrs}
batched_edge_frame = FrameRef(Frame(cols))
super(BatchedDGLGraph, self).__init__(graph_data=batched_index,
node_frame=batched_node_frame,
edge_frame=batched_edge_frame)
# extra members
self._batch_size = 0
self._batch_num_nodes = []
self._batch_num_edges = []
for grh in graph_list:
if isinstance(grh, BatchedDGLGraph):
# handle the input is again a batched graph.
self._batch_size += grh._batch_size
self._batch_num_nodes += grh._batch_num_nodes
self._batch_num_edges += grh._batch_num_edges
else:
self._batch_size += 1
self._batch_num_nodes.append(grh.number_of_nodes())
self._batch_num_edges.append(grh.number_of_edges())
@property
def batch_size(self):
"""Number of graphs in this batch.
Returns
-------
int
Number of graphs in this batch."""
return self._batch_size
@property
def batch_num_nodes(self):
"""Number of nodes of each graph in this batch.
Returns
-------
list
Number of nodes of each graph in this batch."""
return self._batch_num_nodes
@property
def batch_num_edges(self):
"""Number of edges of each graph in this batch.
Returns
-------
list
Number of edges of each graph in this batch."""
return self._batch_num_edges
# override APIs
def add_nodes(self, num, data=None):
"""Add nodes. Disabled because BatchedDGLGraph is read-only."""
raise DGLError('Readonly graph. Mutation is not allowed.')
def add_edge(self, u, v, data=None):
"""Add one edge. Disabled because BatchedDGLGraph is read-only."""
raise DGLError('Readonly graph. Mutation is not allowed.')
def add_edges(self, u, v, data=None):
"""Add many edges. Disabled because BatchedDGLGraph is read-only."""
raise DGLError('Readonly graph. Mutation is not allowed.')
# new APIs
def __getitem__(self, idx):
"""Slice the batch and return the batch of graphs specified by the idx."""
# TODO
raise NotImplementedError
def __setitem__(self, idx, val):
"""Set the value of the slice. The graph size cannot be changed."""
# TODO
raise NotImplementedError
def split(graph_batch, num_or_size_splits): # pylint: disable=unused-argument
"""Split the batch."""
# TODO(minjie): could follow torch.split syntax
raise NotImplementedError
[docs]def unbatch(graph):
"""Return the list of graphs in this batch.
Parameters
----------
graph : BatchedDGLGraph
The batched graph.
Returns
-------
list
A list of :class:`~dgl.DGLGraph` objects whose attributes are obtained
by partitioning the attributes of the :attr:`graph`. The length of the
list is the same as the batch size of :attr:`graph`.
Notes
-----
Unbatching will break each field tensor of the batched graph into smaller
partitions.
For simpler tasks such as node/edge state aggregation, try to use
readout functions.
See Also
--------
batch
"""
assert isinstance(graph, BatchedDGLGraph)
bsize = graph.batch_size
bnn = graph.batch_num_nodes
bne = graph.batch_num_edges
pttns = gi.disjoint_partition(graph._graph, utils.toindex(bnn))
# split the frames
node_frames = [FrameRef(Frame(num_rows=n)) for n in bnn]
edge_frames = [FrameRef(Frame(num_rows=n)) for n in bne]
for attr, col in graph._node_frame.items():
col_splits = F.split(col, bnn, dim=0)
for i in range(bsize):
node_frames[i][attr] = col_splits[i]
for attr, col in graph._edge_frame.items():
col_splits = F.split(col, bne, dim=0)
for i in range(bsize):
edge_frames[i][attr] = col_splits[i]
return [DGLGraph(graph_data=pttns[i],
node_frame=node_frames[i],
edge_frame=edge_frames[i]) for i in range(bsize)]
[docs]def batch(graph_list, node_attrs=ALL, edge_attrs=ALL):
"""Batch a collection of :class:`~dgl.DGLGraph` and return a
:class:`BatchedDGLGraph` object that is independent of the :attr:`graph_list`.
Parameters
----------
graph_list : iterable
A collection of :class:`~dgl.DGLGraph` to be batched.
node_attrs : None, str or iterable
The node attributes to be batched. If ``None``, the :class:`BatchedDGLGraph`
object will not have any node attributes. By default, all node attributes will
be batched. If ``str`` or iterable, this should specify exactly what node
attributes to be batched.
edge_attrs : None, str or iterable, optional
Same as for the case of :attr:`node_attrs`
Returns
-------
BatchedDGLGraph
one single batched graph
See Also
--------
BatchedDGLGraph
unbatch
"""
return BatchedDGLGraph(graph_list, node_attrs, edge_attrs)
READOUT_ON_ATTRS = {
'nodes': ('ndata', 'batch_num_nodes', 'number_of_nodes'),
'edges': ('edata', 'batch_num_edges', 'number_of_edges'),
}
def _sum_on(graph, typestr, feat, weight):
"""Internal function to sum node or edge features.
Parameters
----------
graph : DGLGraph
The graph.
typestr : str
'nodes' or 'edges'
feat : str
The feature field name.
weight : str
The weight field name.
Returns
-------
Tensor
The (weighted) summed node or edge features.
"""
data_attr, batch_num_objs_attr, _ = READOUT_ON_ATTRS[typestr]
data = getattr(graph, data_attr)
feat = data[feat]
if weight is not None:
weight = data[weight]
weight = F.reshape(weight, (-1,) + (1,) * (F.ndim(feat) - 1))
feat = weight * feat
if isinstance(graph, BatchedDGLGraph):
n_graphs = graph.batch_size
batch_num_objs = getattr(graph, batch_num_objs_attr)
seg_id = F.zerocopy_from_numpy(np.arange(n_graphs, dtype='int64').repeat(batch_num_objs))
seg_id = F.copy_to(seg_id, F.context(feat))
y = F.unsorted_1d_segment_sum(feat, seg_id, n_graphs, 0)
return y
else:
return F.sum(feat, 0)
[docs]def sum_nodes(graph, feat, weight=None):
"""Sums all the values of node field :attr:`feat` in :attr:`graph`, optionally
multiplies the field by a scalar node field :attr:`weight`.
Parameters
----------
graph : DGLGraph.
The graph.
feat : str
The feature field.
weight : str, optional
The weight field. If None, no weighting will be performed,
otherwise, weight each node feature with field :attr:`feat`.
for summation. The weight feature associated in the :attr:`graph`
should be a tensor of shape ``[graph.number_of_nodes(), 1]``.
Returns
-------
tensor
The summed tensor.
Notes
-----
If graph is a :class:`BatchedDGLGraph` object, a stacked tensor is
returned instead, i.e. having an extra first dimension.
Each row of the stacked tensor contains the readout result of the
corresponding example in the batch. If an example has no nodes,
a zero tensor with the same shape is returned at the corresponding row.
Examples
--------
>>> import dgl
>>> import torch as th
Create two :class:`~dgl.DGLGraph` objects and initialize their
node features.
>>> g1 = dgl.DGLGraph() # Graph 1
>>> g1.add_nodes(2)
>>> g1.ndata['h'] = th.tensor([[1.], [2.]])
>>> g1.ndata['w'] = th.tensor([[3.], [6.]])
>>> g2 = dgl.DGLGraph() # Graph 2
>>> g2.add_nodes(3)
>>> g2.ndata['h'] = th.tensor([[1.], [2.], [3.]])
Sum over node attribute :attr:`h` without weighting for each graph in a
batched graph.
>>> bg = dgl.batch([g1, g2], node_attrs='h')
>>> dgl.sum_nodes(bg, 'h')
tensor([[3.], # 1 + 2
[6.]]) # 1 + 2 + 3
Sum node attribute :attr:`h` with weight from node attribute :attr:`w`
for a single graph.
>>> dgl.sum_nodes(g1, 'h', 'w')
tensor([15.]) # 1 * 3 + 2 * 6
See Also
--------
mean_nodes
sum_edges
mean_edges
"""
return _sum_on(graph, 'nodes', feat, weight)
[docs]def sum_edges(graph, feat, weight=None):
"""Sums all the values of edge field :attr:`feat` in :attr:`graph`,
optionally multiplies the field by a scalar edge field :attr:`weight`.
Parameters
----------
graph : DGLGraph
The graph.
feat : str
The feature field.
weight : str, optional
The weight field. If None, no weighting will be performed,
otherwise, weight each edge feature with field :attr:`feat`.
for summation. The weight feature associated in the :attr:`graph`
should be a tensor of shape ``[graph.number_of_edges(), 1]``.
Returns
-------
tensor
The summed tensor.
Notes
-----
If graph is a :class:`BatchedDGLGraph` object, a stacked tensor is
returned instead, i.e. having an extra first dimension.
Each row of the stacked tensor contains the readout result of the
corresponding example in the batch. If an example has no edges,
a zero tensor with the same shape is returned at the corresponding row.
Examples
--------
>>> import dgl
>>> import torch as th
Create two :class:`~dgl.DGLGraph` objects and initialize their
edge features.
>>> g1 = dgl.DGLGraph() # Graph 1
>>> g1.add_nodes(2)
>>> g1.add_edges([0, 1], [1, 0])
>>> g1.edata['h'] = th.tensor([[1.], [2.]])
>>> g1.edata['w'] = th.tensor([[3.], [6.]])
>>> g2 = dgl.DGLGraph() # Graph 2
>>> g2.add_nodes(3)
>>> g2.add_edges([0, 1, 2], [1, 2, 0])
>>> g2.edata['h'] = th.tensor([[1.], [2.], [3.]])
Sum over edge attribute :attr:`h` without weighting for each graph in a
batched graph.
>>> bg = dgl.batch([g1, g2], edge_attrs='h')
>>> dgl.sum_edges(bg, 'h')
tensor([[3.], # 1 + 2
[6.]]) # 1 + 2 + 3
Sum edge attribute :attr:`h` with weight from edge attribute :attr:`w`
for a single graph.
>>> dgl.sum_edges(g1, 'h', 'w')
tensor([15.]) # 1 * 3 + 2 * 6
See Also
--------
sum_nodes
mean_nodes
mean_edges
"""
return _sum_on(graph, 'edges', feat, weight)
def _mean_on(graph, typestr, feat, weight):
"""Internal function to sum node or edge features.
Parameters
----------
graph : DGLGraph
The graph.
typestr : str
'nodes' or 'edges'
feat : str
The feature field name.
weight : str
The weight field name.
Returns
-------
Tensor
The (weighted) summed node or edge features.
"""
data_attr, batch_num_objs_attr, _ = READOUT_ON_ATTRS[typestr]
data = getattr(graph, data_attr)
feat = data[feat]
if weight is not None:
weight = data[weight]
weight = F.reshape(weight, (-1,) + (1,) * (F.ndim(feat) - 1))
feat = weight * feat
if isinstance(graph, BatchedDGLGraph):
n_graphs = graph.batch_size
batch_num_objs = getattr(graph, batch_num_objs_attr)
seg_id = F.zerocopy_from_numpy(np.arange(n_graphs, dtype='int64').repeat(batch_num_objs))
seg_id = F.copy_to(seg_id, F.context(feat))
if weight is not None:
w = F.unsorted_1d_segment_sum(weight, seg_id, n_graphs, 0)
y = F.unsorted_1d_segment_sum(feat, seg_id, n_graphs, 0)
y = y / w
else:
y = F.unsorted_1d_segment_mean(feat, seg_id, n_graphs, 0)
return y
else:
if weight is None:
return F.mean(feat, 0)
else:
y = F.sum(feat, 0) / F.sum(weight, 0)
return y
[docs]def mean_nodes(graph, feat, weight=None):
"""Averages all the values of node field :attr:`feat` in :attr:`graph`,
optionally multiplies the field by a scalar node field :attr:`weight`.
Parameters
----------
graph : DGLGraph or BatchedDGLGraph
The graph.
feat : str
The feature field.
weight : str, optional
The weight field. If None, no weighting will be performed,
otherwise, weight each node feature with field :attr:`feat`.
for calculating mean. The weight feature associated in the :attr:`graph`
should be a tensor of shape ``[graph.number_of_nodes(), 1]``.
Returns
-------
tensor
The averaged tensor.
Notes
-----
If graph is a :class:`BatchedDGLGraph` object, a stacked tensor is
returned instead, i.e. having an extra first dimension.
Each row of the stacked tensor contains the readout result of
corresponding example in the batch. If an example has no nodes,
a zero tensor with the same shape is returned at the corresponding row.
Examples
--------
>>> import dgl
>>> import torch as th
Create two :class:`~dgl.DGLGraph` objects and initialize their
node features.
>>> g1 = dgl.DGLGraph() # Graph 1
>>> g1.add_nodes(2)
>>> g1.ndata['h'] = th.tensor([[1.], [2.]])
>>> g1.ndata['w'] = th.tensor([[3.], [6.]])
>>> g2 = dgl.DGLGraph() # Graph 2
>>> g2.add_nodes(3)
>>> g2.ndata['h'] = th.tensor([[1.], [2.], [3.]])
Average over node attribute :attr:`h` without weighting for each graph in a
batched graph.
>>> bg = dgl.batch([g1, g2], node_attrs='h')
>>> dgl.mean_nodes(bg, 'h')
tensor([[1.5000], # (1 + 2) / 2
[2.0000]]) # (1 + 2 + 3) / 3
Sum node attribute :attr:`h` with normalized weight from node attribute :attr:`w`
for a single graph.
>>> dgl.mean_nodes(g1, 'h', 'w') # h1 * (w1 / (w1 + w2)) + h2 * (w2 / (w1 + w2))
tensor([1.6667]) # 1 * (3 / (3 + 6)) + 2 * (6 / (3 + 6))
See Also
--------
sum_nodes
sum_edges
mean_edges
"""
return _mean_on(graph, 'nodes', feat, weight)
[docs]def mean_edges(graph, feat, weight=None):
"""Averages all the values of edge field :attr:`feat` in :attr:`graph`,
optionally multiplies the field by a scalar edge field :attr:`weight`.
Parameters
----------
graph : DGLGraph
The graph.
feat : str
The feature field.
weight : optional, str
The weight field. If None, no weighting will be performed,
otherwise, weight each edge feature with field :attr:`feat`.
for calculating mean. The weight feature associated in the :attr:`graph`
should be a tensor of shape ``[graph.number_of_edges(), 1]``.
Returns
-------
tensor
The averaged tensor.
Notes
-----
If graph is a :class:`BatchedDGLGraph` object, a stacked tensor is
returned instead, i.e. having an extra first dimension.
Each row of the stacked tensor contains the readout result of
corresponding example in the batch. If an example has no edges,
a zero tensor with the same shape is returned at the corresponding row.
Examples
--------
>>> import dgl
>>> import torch as th
Create two :class:`~dgl.DGLGraph` objects and initialize their
edge features.
>>> g1 = dgl.DGLGraph() # Graph 1
>>> g1.add_nodes(2)
>>> g1.add_edges([0, 1], [1, 0])
>>> g1.edata['h'] = th.tensor([[1.], [2.]])
>>> g1.edata['w'] = th.tensor([[3.], [6.]])
>>> g2 = dgl.DGLGraph() # Graph 2
>>> g2.add_nodes(3)
>>> g2.add_edges([0, 1, 2], [1, 2, 0])
>>> g2.edata['h'] = th.tensor([[1.], [2.], [3.]])
Average over edge attribute :attr:`h` without weighting for each graph in a
batched graph.
>>> bg = dgl.batch([g1, g2], edge_attrs='h')
>>> dgl.mean_edges(bg, 'h')
tensor([[1.5000], # (1 + 2) / 2
[2.0000]]) # (1 + 2 + 3) / 3
Sum edge attribute :attr:`h` with normalized weight from edge attribute :attr:`w`
for a single graph.
>>> dgl.mean_edges(g1, 'h', 'w') # h1 * (w1 / (w1 + w2)) + h2 * (w2 / (w1 + w2))
tensor([1.6667]) # 1 * (3 / (3 + 6)) + 2 * (6 / (3 + 6))
See Also
--------
sum_nodes
mean_nodes
sum_edges
"""
return _mean_on(graph, 'edges', feat, weight)
def _max_on(graph, typestr, feat):
"""Internal function to take elementwise maximum
over node or edge features.
Parameters
----------
graph : DGLGraph
The graph.
typestr : str
'nodes' or 'edges'
feat : str
The feature field name.
Returns
-------
Tensor
The (weighted) summed node or edge features.
"""
data_attr, batch_num_objs_attr, _ = READOUT_ON_ATTRS[typestr]
data = getattr(graph, data_attr)
feat = data[feat]
if isinstance(graph, BatchedDGLGraph):
batch_num_objs = getattr(graph, batch_num_objs_attr)
max_readout_list = []
first = 0
for num_obj in batch_num_objs:
if num_obj == 0:
max_readout_list.append(F.zeros(F.shape(feat)[1:],
F.dtype(feat),
F.context(feat)))
continue
max_readout_list.append(F.max(feat[first:first+num_obj], 0))
first += num_obj
return F.stack(max_readout_list, 0)
else:
return F.max(feat, 0)
[docs]def max_nodes(graph, feat):
"""Take elementwise maximum over all the values of node field
:attr:`feat` in :attr:`graph`
Parameters
----------
graph : DGLGraph or BatchedDGLGraph
The graph.
feat : str
The feature field.
Returns
-------
tensor
The tensor obtained.
Notes
-----
If graph is a :class:`BatchedDGLGraph` object, a stacked tensor is
returned instead, i.e. having an extra first dimension.
Each row of the stacked tensor contains the readout result of
corresponding example in the batch. If an example has no nodes,
a zero tensor with the same shape is returned at the corresponding row.
"""
return _max_on(graph, 'nodes', feat)
[docs]def max_edges(graph, feat):
"""Take elementwise maximum over all the values of edge field
:attr:`feat` in :attr:`graph`
Parameters
----------
graph : DGLGraph or BatchedDGLGraph
The graph.
feat : str
The feature field.
Returns
-------
tensor
The tensor obtained.
Notes
-----
If graph is a :class:`BatchedDGLGraph` object, a stacked tensor is
returned instead, i.e. having an extra first dimension.
Each row of the stacked tensor contains the readout result of
corresponding example in the batch. If an example has no edges,
a zero tensor with the same shape is returned at the corresponding row.
"""
return _max_on(graph, 'edges', feat)