diff --git a/src/graphnet/models/graphs/edges/__init__.py b/src/graphnet/models/graphs/edges/__init__.py
index 7da8baa7c..40c8bbeab 100644
--- a/src/graphnet/models/graphs/edges/__init__.py
+++ b/src/graphnet/models/graphs/edges/__init__.py
@@ -5,3 +5,4 @@
 and their features.
 """
 from .edges import EdgeDefinition, KNNEdges, RadialEdges, EuclideanEdges
+from .minkowski import MinkowskiKNNEdges
diff --git a/src/graphnet/models/graphs/edges/minkowski.py b/src/graphnet/models/graphs/edges/minkowski.py
new file mode 100644
index 000000000..5d1134ec5
--- /dev/null
+++ b/src/graphnet/models/graphs/edges/minkowski.py
@@ -0,0 +1,98 @@
+"""Module containing EdgeDefinitions based on the Minkowski Metric."""
+from typing import Optional, List
+
+import torch
+from torch_geometric.data import Data
+from torch_geometric.utils import to_dense_batch
+from graphnet.models.graphs.edges.edges import EdgeDefinition
+
+
+def compute_minkowski_distance_mat(
+    x: torch.Tensor,
+    y: torch.Tensor,
+    c: float,
+    space_coords: Optional[List[int]] = None,
+    time_coord: Optional[int] = 3,
+) -> torch.Tensor:
+    """Compute all pairwise Minkowski distances.
+
+    Args:
+        x: First tensor of shape (n, d).
+        y: Second tensor of shape (m, d).
+        c: Speed of light, in scaled units.
+        space_coords: Indices of space coordinates.
+        time_coord: Index of time coordinate.
+
+    Returns: Matrix of shape (n, m) of all pairwise Minkowski distances.
+    """
+    space_coords = space_coords or [0, 1, 2]
+    assert x.dim() == 2, "x must be 2-dimensional"
+    assert y.dim() == 2, "x must be 2-dimensional"
+    dist = x[:, None] - y[None, :]
+    pos = dist[:, :, space_coords]
+    time = dist[:, :, time_coord] * c
+    return (pos**2).sum(dim=-1) - time**2
+
+
+class MinkowskiKNNEdges(EdgeDefinition):
+    """Builds edges between most light-like separated."""
+
+    def __init__(
+        self,
+        nb_nearest_neighbours: int,
+        c: float,
+        time_like_weight: float = 1.0,
+        space_coords: Optional[List[int]] = None,
+        time_coord: Optional[int] = 3,
+    ):
+        """Initialize MinkowskiKNNEdges.
+
+        Args:
+            nb_nearest_neighbours: Number of neighbours to connect to.
+            c: Speed of light, in scaled units.
+            time_like_weight: Preference to time-like over space-like edges.
+                Scales time_like distances by this value, before finding
+                nearest neighbours.
+            space_coords: Coordinates of x, y, z.
+            time_coord: Coordinate of time.
+        """
+        super().__init__(name=__name__, class_name=self.__class__.__name__)
+        self.nb_nearest_neighbours = nb_nearest_neighbours
+        self.c = c
+        self.time_like_weight = time_like_weight
+        self.space_coords = space_coords or [0, 1, 2]
+        self.time_coord = time_coord
+
+    def _construct_edges(self, graph: Data) -> Data:
+        x, mask = to_dense_batch(graph.x, graph.batch)
+        count = 0
+        row = []
+        col = []
+        for batch in range(x.shape[0]):
+            distance_mat = compute_minkowski_distance_mat(
+                x_masked := x[batch][mask[batch]],
+                x_masked,
+                self.c,
+                self.space_coords,
+                self.time_coord,
+            )
+            num_points = x_masked.shape[0]
+            num_edges = min(self.nb_nearest_neighbours, num_points)
+            col += [
+                c
+                for c in range(num_points)
+                for _ in range(count, count + num_edges)
+            ]
+            distance_mat[distance_mat < 0] *= -self.time_like_weight
+            distance_mat += (
+                torch.eye(distance_mat.shape[0]) * 1e9
+            )  # self-loops
+            distance_sorted = distance_mat.argsort(dim=1)
+            distance_sorted += count  # offset by previous events
+            row += distance_sorted[:num_edges].flatten().tolist()
+            count += num_points
+
+        graph.edge_index = torch.tensor(
+            [row, col], dtype=torch.long, device=graph.x.device
+        )
+        return graph
diff --git a/tests/models/test_minkowski.py b/tests/models/test_minkowski.py
new file mode 100644
index 000000000..af66196cf
--- /dev/null
+++ b/tests/models/test_minkowski.py
@@ -0,0 +1,160 @@
+"""Unit tests for minkowski based edges."""
+import pytest
+import torch
+from torch_geometric.data.data import Data
+
+from graphnet.models.graphs.edges import KNNEdges, MinkowskiKNNEdges
+from graphnet.models.graphs.edges.minkowski import (
+    compute_minkowski_distance_mat,
+)
+
+
+def test_compute_minkowski_distance_mat() -> None:
+    """Testing the computation of the Minkowski distance matrix."""
+    vec1 = torch.tensor(
+        [
+            [
+                0.0,
+                0.0,
+                0.0,
+                0.0,
+            ],
+            [
+                0.0,
+                0.0,
+                1.0,
+                1.0,
+            ],
+            [
+                1.0,
+                0.0,
+                0.0,
+                1.0,
+            ],
+            [
+                1.0,
+                0.0,
+                1.0,
+                2.0,
+            ],
+        ]
+    )
+    vec2 = torch.tensor(
+        [
+            [
+                0.0,
+                0.0,
+                0.0,
+                -1.0,
+            ],
+            [
+                1.0,
+                1.0,
+                1.0,
+                0.0,
+            ],
+        ]
+    )
+    expected11 = torch.tensor(
+        [
+            [
+                0.0,
+                0.0,
+                0.0,
+                -2.0,
+            ],
+            [
+                0.0,
+                0.0,
+                2.0,
+                0.0,
+            ],
+            [
+                0.0,
+                2.0,
+                0.0,
+                0.0,
+            ],
+            [
+                -2.0,
+                0.0,
+                0.0,
+                0.0,
+            ],
+        ]
+    )
+    expected12 = torch.tensor(
+        [[-1.0, 3.0], [-3.0, 1.0], [-3.0, 1.0], [-7.0, -3.0]]
+    )
+    expected22 = torch.tensor(
+        [
+            [0.0, 2.0],
+            [2.0, 0.0],
+        ]
+    )
+    mat11 = compute_minkowski_distance_mat(vec1, vec1, c=1.0)
+    mat12 = compute_minkowski_distance_mat(vec1, vec2, c=1.0)
+    mat22 = compute_minkowski_distance_mat(vec2, vec2, c=1.0)
+
+    assert torch.allclose(mat11, expected11)
+    assert torch.allclose(mat12, expected12)
+    assert torch.allclose(mat22, expected22)
+
+
+def test_minkowski_knn_edges() -> None:
+    """Testing the minkowski knn edge definition."""
+    data = Data(
+        x=torch.tensor(
+            [
+                [
+                    0.0,
+                    0.0,
+                    0.0,
+                    0.0,
+                ],
+                [
+                    0.0,
+                    0.0,
+                    1.0,
+                    1.0,
+                ],
+                [
+                    1.0,
+                    0.0,
+                    0.0,
+                    1.0,
+                ],
+                [
+                    1.0,
+                    0.0,
+                    1.0,
+                    2.0,
+                ],
+            ]
+        )
+    )
+    edge_index = MinkowskiKNNEdges(
+        nb_nearest_neighbours=2,
+        c=1.0,
+    )(data).edge_index
+    expected = torch.tensor(
+        [
+            [1, 2, 0, 3, 0, 3, 1, 2],
+            [0, 0, 1, 1, 2, 2, 3, 3],
+        ]
+    )
+    assert torch.allclose(edge_index[1], expected[1])
+
+    # Allow for "permutation of connections" in edge_index[1]
+    assert torch.allclose(
+        edge_index[0, [0, 1]], expected[0, [0, 1]]
+    ) or torch.allclose(edge_index[1, [0, 1]], expected[1, [1, 0]])
+    assert torch.allclose(
+        edge_index[0, [2, 3]], expected[0, [2, 3]]
+    ) or torch.allclose(edge_index[1, [2, 3]], expected[1, [3, 2]])
+    assert torch.allclose(
+        edge_index[0, [4, 5]], expected[0, [4, 5]]
+    ) or torch.allclose(edge_index[1, [4, 5]], expected[1, [5, 4]])
+    assert torch.allclose(
+        edge_index[0, [6, 7]], expected[0, [6, 7]]
+    ) or torch.allclose(edge_index[1, [6, 7]], expected[1, [7, 6]])