diff --git a/CHANGELOG.md b/CHANGELOG.md
index 38edaa119be5..901bb4c99644 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,7 +7,7 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ### Added
 
-- Added `torch_geometric.Index` ([#9276](https://github.com/pyg-team/pytorch_geometric/pull/9276), [#9277](https://github.com/pyg-team/pytorch_geometric/pull/9277))
+- Added `torch_geometric.Index` ([#9276](https://github.com/pyg-team/pytorch_geometric/pull/9276), [#9277](https://github.com/pyg-team/pytorch_geometric/pull/9277), [#9278](https://github.com/pyg-team/pytorch_geometric/pull/9278))
 - Added support for PyTorch 2.3 ([#9240](https://github.com/pyg-team/pytorch_geometric/pull/9240))
 - Added support for `EdgeIndex` in `message_and_aggregate` ([#9131](https://github.com/pyg-team/pytorch_geometric/pull/9131))
 - Added `CornellTemporalHyperGraphDataset` ([#9090](https://github.com/pyg-team/pytorch_geometric/pull/9090))
diff --git a/test/test_index.py b/test/test_index.py
index c9928a4a76a7..8b2b34cbb46b 100644
--- a/test/test_index.py
+++ b/test/test_index.py
@@ -1,5 +1,6 @@
 import pytest
 import torch
+from torch import tensor
 
 from torch_geometric import Index
 from torch_geometric.testing import withCUDA
@@ -54,3 +55,36 @@ def test_identity(dtype, device):
     out = Index(index, dim_size=4, is_sorted=False)
     assert out.dim_size == 4
     assert out.is_sorted == index.is_sorted
+
+
+def test_validate():
+    with pytest.raises(ValueError, match="unsupported data type"):
+        Index([0.0, 1.0])
+    with pytest.raises(ValueError, match="needs to be one-dimensional"):
+        Index([[0], [1]])
+    with pytest.raises(TypeError, match="invalid combination of arguments"):
+        Index(torch.tensor([0, 1]), torch.long)
+    with pytest.raises(TypeError, match="invalid keyword arguments"):
+        Index(torch.tensor([0, 1]), dtype=torch.long)
+    with pytest.raises(ValueError, match="contains negative indices"):
+        Index([-1, 0]).validate()
+    with pytest.raises(ValueError, match="than its registered size"):
+        Index([0, 10], dim_size=2).validate()
+    with pytest.raises(ValueError, match="not sorted"):
+        Index([1, 0], is_sorted=True).validate()
+
+
+@withCUDA
+@pytest.mark.parametrize('dtype', DTYPES)
+def test_fill_cache_(dtype, device):
+    kwargs = dict(dtype=dtype, device=device)
+    index = Index([0, 1, 1, 2], is_sorted=True, **kwargs)
+    index.validate().fill_cache_()
+    assert index.dim_size == 3
+    assert index._indptr.dtype == dtype
+    assert index._indptr.equal(tensor([0, 1, 3, 4], device=device))
+
+    index = Index([1, 0, 2, 1], **kwargs)
+    index.validate().fill_cache_()
+    assert index.dim_size == 3
+    assert index._indptr is None
diff --git a/torch_geometric/index.py b/torch_geometric/index.py
index 2382ec2ee33c..328257b7d4aa 100644
--- a/torch_geometric/index.py
+++ b/torch_geometric/index.py
@@ -167,6 +167,24 @@ def __new__(
 
     def validate(self) -> 'Index':
         r"""TODO."""
+        assert_valid_dtype(self._data)
+        assert_one_dimensional(self._data)
+        assert_contiguous(self._data)
+
+        if self.numel() > 0 and self._data.min() < 0:
+            raise ValueError(f"'{self.__class__.__name__}' contains negative "
+                             f"indices (got {int(self.min())})")
+
+        if (self.numel() > 0 and self.dim_size is not None
+                and self._data.max() >= self.dim_size):
+            raise ValueError(f"'{self.__class__.__name__}' contains larger "
+                             f"indices than its registered size "
+                             f"(got {int(self._data.max())}, but expected "
+                             f"values smaller than {self.dim_size})")
+
+        if self.is_sorted and (self._data.diff() < 0).any():
+            raise ValueError(f"'{self.__class__.__name__}' is not sorted")
+
         return self
 
     # Properties ##############################################################
@@ -185,20 +203,34 @@ def is_sorted(self) -> bool:
 
     def get_dim_size(self) -> int:
         r"""TODO."""
-        raise NotImplementedError
+        if self._dim_size is None:
+            dim_size = int(self._data.max()) + 1 if self.numel() > 0 else 0
+            self._dim_size = dim_size
+
+        assert isinstance(self._dim_size, int)
+        return self._dim_size
 
     def dim_resize_(self, dim_size: Optional[int]) -> 'Index':
         r"""TODO."""
-        raise NotImplementedError
+        raise NotImplementedError  # TODO
 
     @assert_sorted
     def get_indptr(self) -> Tensor:
         r"""TODO."""
-        raise NotImplementedError
+        if self._indptr is None:
+            self._indptr = index2ptr(self._data, self.get_dim_size())
+
+        assert isinstance(self._indptr, Tensor)
+        return self._indptr
 
     def fill_cache_(self) -> 'Index':
         r"""TODO."""
-        raise NotImplementedError
+        self.get_dim_size()
+
+        if self.is_sorted:
+            self.get_indptr()
+
+        return self
 
     # Methods #################################################################
 
@@ -219,7 +251,7 @@ def as_tensor(self) -> Tensor:
 
     def dim_narrow(self, start: Union[int, Tensor], length: int) -> 'Index':
         r"""TODO."""
-        raise NotImplementedError
+        raise NotImplementedError  # TODO
 
     # PyTorch/Python builtins #################################################