diff --git a/CHANGELOG.md b/CHANGELOG.md
index e9424a4624fb..3a06934bed42 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ## [2.0.5] - 2022-MM-DD
 ### Added
+- Added faster initialization of `NeighborLoader` in case edge indices are already sorted (via `is_sorted=True`) ([#4620](https://github.com/pyg-team/pytorch_geometric/pull/4620))
 - Added `AddPositionalEncoding` transform ([#4521](https://github.com/pyg-team/pytorch_geometric/pull/4521))
 - Added `HeteroData.is_undirected()` support ([#4604](https://github.com/pyg-team/pytorch_geometric/pull/4604))
 - Added the `Genius` and `Wiki` datasets to `nn.datasets.LINKXDataset` ([#4570](https://github.com/pyg-team/pytorch_geometric/pull/4570), [#4600](https://github.com/pyg-team/pytorch_geometric/pull/4600))
diff --git a/torch_geometric/data/lightning_datamodule.py b/torch_geometric/data/lightning_datamodule.py
index 550784a57762..cafe28d4c77a 100644
--- a/torch_geometric/data/lightning_datamodule.py
+++ b/torch_geometric/data/lightning_datamodule.py
@@ -274,6 +274,7 @@ def __init__(
                 directed=kwargs.get('directed', True),
                 input_type=get_input_nodes(data, input_train_nodes)[0],
                 time_attr=kwargs.get('time_attr', None),
+                is_sorted=kwargs.get('is_sorted', False),
             )
         self.input_train_nodes = input_train_nodes
         self.input_val_nodes = input_val_nodes
diff --git a/torch_geometric/loader/link_neighbor_loader.py b/torch_geometric/loader/link_neighbor_loader.py
index 08390100e2f0..e8162ea66fd9 100644
--- a/torch_geometric/loader/link_neighbor_loader.py
+++ b/torch_geometric/loader/link_neighbor_loader.py
@@ -201,9 +201,6 @@ class LinkNeighborLoader(torch.utils.data.DataLoader):
             replacement. (default: :obj:`False`)
         directed (bool, optional): If set to :obj:`False`, will include all
             edges between all sampled nodes. (default: :obj:`True`)
-        transform (Callable, optional): A function/transform that takes in
-            a sampled mini-batch and returns a transformed version.
-            (default: :obj:`None`)
         neg_sampling_ratio (float, optional): The ratio of sampled negative
             edges to the number of positive edges.
             If :obj:`edge_label` does not exist, it will be automatically
@@ -219,6 +216,13 @@ class LinkNeighborLoader(torch.utils.data.DataLoader):
             :meth:`F.binary_cross_entropy`) and of type
             :obj:`torch.long` for multi-class classification (to facilitate the
             ease-of-use of :meth:`F.cross_entropy`). (default: :obj:`0.0`).
+        transform (Callable, optional): A function/transform that takes in
+            a sampled mini-batch and returns a transformed version.
+            (default: :obj:`None`)
+        is_sorted (bool, optional): If set to :obj:`True`, assumes that
+            :obj:`edge_index` is sorted by column. This avoids internal
+            re-sorting of the data and can improve runtime and memory
+            efficiency. (default: :obj:`False`)
         **kwargs (optional): Additional arguments of
             :class:`torch.utils.data.DataLoader`, such as :obj:`batch_size`,
             :obj:`shuffle`, :obj:`drop_last` or :obj:`num_workers`.
@@ -231,9 +235,10 @@ def __init__(
         edge_label: OptTensor = None,
         replace: bool = False,
         directed: bool = True,
+        neg_sampling_ratio: float = 0.0,
         transform: Callable = None,
+        is_sorted: bool = False,
         neighbor_sampler: Optional[LinkNeighborSampler] = None,
-        neg_sampling_ratio: float = 0.0,
         **kwargs,
     ):
         # Remove for PyTorch Lightning:
@@ -259,9 +264,15 @@ def __init__(
 
         if neighbor_sampler is None:
             self.neighbor_sampler = LinkNeighborSampler(
-                data, num_neighbors, replace, directed, edge_type,
+                data,
+                num_neighbors,
+                replace,
+                directed,
+                input_type=edge_type,
+                is_sorted=is_sorted,
+                neg_sampling_ratio=self.neg_sampling_ratio,
                 share_memory=kwargs.get('num_workers', 0) > 0,
-                neg_sampling_ratio=self.neg_sampling_ratio)
+            )
 
         super().__init__(Dataset(edge_label_index, edge_label),
                          collate_fn=self.neighbor_sampler, **kwargs)
diff --git a/torch_geometric/loader/neighbor_loader.py b/torch_geometric/loader/neighbor_loader.py
index b7bdf2c505cb..744b6e4d06e5 100644
--- a/torch_geometric/loader/neighbor_loader.py
+++ b/torch_geometric/loader/neighbor_loader.py
@@ -24,8 +24,9 @@ def __init__(
         replace: bool = False,
         directed: bool = True,
         input_type: Optional[Any] = None,
-        share_memory: bool = False,
         time_attr: Optional[str] = None,
+        is_sorted: bool = False,
+        share_memory: bool = False,
     ):
         self.data_cls = data.__class__
         self.num_neighbors = num_neighbors
@@ -41,7 +42,8 @@ def __init__(
                     f"'{data.__class__.__name__}' object")
 
             # Convert the graph data into a suitable format for sampling.
-            out = to_csc(data, device='cpu', share_memory=share_memory)
+            out = to_csc(data, device='cpu', share_memory=share_memory,
+                         is_sorted=is_sorted)
             self.colptr, self.row, self.perm = out
             assert isinstance(num_neighbors, (list, tuple))
 
@@ -54,7 +56,8 @@ def __init__(
             # Convert the graph data into a suitable format for sampling.
             # NOTE: Since C++ cannot take dictionaries with tuples as key as
             # input, edge type triplets are converted into single strings.
-            out = to_hetero_csc(data, device='cpu', share_memory=share_memory)
+            out = to_hetero_csc(data, device='cpu', share_memory=share_memory,
+                                is_sorted=is_sorted)
             self.colptr_dict, self.row_dict, self.perm_dict = out
 
             self.node_types, self.edge_types = data.metadata()
@@ -245,6 +248,10 @@ class NeighborLoader(torch.utils.data.DataLoader):
         transform (Callable, optional): A function/transform that takes in
             a sampled mini-batch and returns a transformed version.
             (default: :obj:`None`)
+        is_sorted (bool, optional): If set to :obj:`True`, assumes that
+            :obj:`edge_index` is sorted by column. This avoids internal
+            re-sorting of the data and can improve runtime and memory
+            efficiency. (default: :obj:`False`)
         **kwargs (optional): Additional arguments of
             :class:`torch.utils.data.DataLoader`, such as :obj:`batch_size`,
             :obj:`shuffle`, :obj:`drop_last` or :obj:`num_workers`.
@@ -258,6 +265,7 @@ def __init__(
         directed: bool = True,
         time_attr: Optional[str] = None,
         transform: Callable = None,
+        is_sorted: bool = False,
         neighbor_sampler: Optional[NeighborSampler] = None,
         **kwargs,
     ):
@@ -281,9 +289,15 @@ def __init__(
 
         if neighbor_sampler is None:
             self.neighbor_sampler = NeighborSampler(
-                data, num_neighbors, replace, directed, node_type,
+                data,
+                num_neighbors,
+                replace,
+                directed,
+                input_type=node_type,
                 time_attr=time_attr,
-                share_memory=kwargs.get('num_workers', 0) > 0)
+                is_sorted=is_sorted,
+                share_memory=kwargs.get('num_workers', 0) > 0,
+            )
 
         super().__init__(input_nodes, collate_fn=self.neighbor_sampler,
                          **kwargs)
diff --git a/torch_geometric/loader/utils.py b/torch_geometric/loader/utils.py
index a7b783727477..e69ae0c0c9d3 100644
--- a/torch_geometric/loader/utils.py
+++ b/torch_geometric/loader/utils.py
@@ -34,6 +34,7 @@ def to_csc(
     data: Union[Data, EdgeStorage],
     device: Optional[torch.device] = None,
     share_memory: bool = False,
+    is_sorted: bool = False,
 ) -> Tuple[Tensor, Tensor, OptTensor]:
     # Convert the graph data into a suitable format for sampling (CSC format).
     # Returns the `colptr` and `row` indices of the graph, as well as an
@@ -47,17 +48,18 @@ def to_csc(
 
     elif hasattr(data, 'edge_index'):
         (row, col) = data.edge_index
-        size = data.size()
-        perm = (col * size[0]).add_(row).argsort()
+        if not is_sorted:
+            size = data.size()
+            perm = (col * size[0]).add_(row).argsort()
+            row = row[perm]
         colptr = torch.ops.torch_sparse.ind2ptr(col[perm], size[1])
-        row = row[perm]
     else:
         raise AttributeError("Data object does not contain attributes "
                              "'adj_t' or 'edge_index'")
 
     colptr = colptr.to(device)
     row = row.to(device)
-    perm = perm if perm is not None else perm.to(device)
+    perm = perm.to(device) if perm is not None else None
 
     if not colptr.is_cuda and share_memory:
         colptr.share_memory_()
@@ -72,6 +74,7 @@ def to_hetero_csc(
     data: HeteroData,
     device: Optional[torch.device] = None,
     share_memory: bool = False,
+    is_sorted: bool = False,
 ) -> Tuple[Dict[str, Tensor], Dict[str, Tensor], Dict[str, OptTensor]]:
     # Convert the heterogeneous graph data into a suitable format for sampling
     # (CSC format).
@@ -83,7 +86,7 @@ def to_hetero_csc(
 
     for store in data.edge_stores:
         key = edge_type_to_str(store._key)
-        out = to_csc(store, device, share_memory)
+        out = to_csc(store, device, share_memory, is_sorted)
         colptr_dict[key], row_dict[key], perm_dict[key] = out
 
     return colptr_dict, row_dict, perm_dict