diff --git a/pina/graph.py b/pina/graph.py
index 1340ed69a..201f37a24 100644
--- a/pina/graph.py
+++ b/pina/graph.py
@@ -3,6 +3,7 @@
 import torch
 from torch_geometric.data import Data, Batch
 from torch_geometric.utils import to_undirected
+from torch_geometric.utils.loop import remove_self_loops
 from .label_tensor import LabelTensor
 from .utils import check_consistency, is_function
 
@@ -209,6 +210,7 @@ def __new__(
         x=None,
         edge_attr=False,
         custom_edge_func=None,
+        loop=True,
         **kwargs,
     ):
         """
@@ -224,18 +226,19 @@ def __new__(
         :param x: Optional tensor of node features of shape ``(N, F)``, where
             ``F`` is the number of features per node.
         :type x: torch.Tensor | LabelTensor, optional
-        :param edge_attr: Optional tensor of edge attributes of shape ``(E, F)``
-            , where ``F`` is the number of features per edge.
-        :type edge_attr: torch.Tensor, optional
+        :param bool edge_attr: Whether to compute the edge attributes.
         :param custom_edge_func: A custom function to compute edge attributes.
             If provided, overrides ``edge_attr``.
         :type custom_edge_func: Callable, optional
+        :param bool loop: Whether to include self-loops.
         :param kwargs: Additional keyword arguments passed to the
             :class:`~pina.graph.Graph` class constructor.
         :return: A :class:`~pina.graph.Graph` instance constructed using the
             provided information.
         :rtype: Graph
         """
+        if not loop:
+            edge_index = remove_self_loops(edge_index)[0]
         edge_attr = cls._create_edge_attr(
             pos, edge_index, edge_attr, custom_edge_func or cls._build_edge_attr
         )
@@ -374,11 +377,8 @@ def compute_knn_graph(points, neighbours):
             representing the edge indices of the graph.
         :rtype: torch.Tensor
         """
-
         dist = torch.cdist(points, points, p=2)
-        knn_indices = torch.topk(dist, k=neighbours + 1, largest=False).indices[
-            :, 1:
-        ]
+        knn_indices = torch.topk(dist, k=neighbours, largest=False).indices
         row = torch.arange(points.size(0)).repeat_interleave(neighbours)
         col = knn_indices.flatten()
         return torch.stack([row, col], dim=0).as_subclass(torch.Tensor)
diff --git a/tests/test_graph.py b/tests/test_graph.py
index bf053a89f..1ea51cfa3 100644
--- a/tests/test_graph.py
+++ b/tests/test_graph.py
@@ -67,8 +67,9 @@ def test_build_graph(x, pos):
         ),
     ],
 )
-def test_build_radius_graph(x, pos):
-    graph = RadiusGraph(x=x, pos=pos, radius=0.5)
+@pytest.mark.parametrize("loop", [True, False])
+def test_build_radius_graph(x, pos, loop):
+    graph = RadiusGraph(x=x, pos=pos, radius=0.5, loop=loop)
     assert hasattr(graph, "x")
     assert hasattr(graph, "pos")
     assert hasattr(graph, "edge_index")
@@ -84,6 +85,15 @@ def test_build_radius_graph(x, pos):
         assert graph.pos.labels == pos.labels
     else:
         assert isinstance(graph.pos, torch.Tensor)
+    if not loop:
+        assert (
+            len(
+                torch.nonzero(
+                    graph.edge_index[0] == graph.edge_index[1], as_tuple=True
+                )[0]
+            )
+            == 0
+        )  # Detect self loops
 
 
 @pytest.mark.parametrize(
@@ -168,8 +178,9 @@ def test_build_radius_graph_custom_edge_attr(x, pos):
         ),
     ],
 )
-def test_build_knn_graph(x, pos):
-    graph = KNNGraph(x=x, pos=pos, neighbours=2)
+@pytest.mark.parametrize("loop", [True, False])
+def test_build_knn_graph(x, pos, loop):
+    graph = KNNGraph(x=x, pos=pos, neighbours=2, loop=loop)
     assert hasattr(graph, "x")
     assert hasattr(graph, "pos")
     assert hasattr(graph, "edge_index")
@@ -186,6 +197,15 @@ def test_build_knn_graph(x, pos):
     else:
         assert isinstance(graph.pos, torch.Tensor)
     assert graph.edge_attr is None
+    self_loops = len(
+        torch.nonzero(
+            graph.edge_index[0] == graph.edge_index[1], as_tuple=True
+        )[0]
+    )
+    if loop:
+        assert self_loops != 0
+    else:
+        assert self_loops == 0
 
 
 @pytest.mark.parametrize(