diff --git a/city2graph/proximity.py b/city2graph/proximity.py
index db55290..fa2dd17 100644
--- a/city2graph/proximity.py
+++ b/city2graph/proximity.py
@@ -919,8 +919,9 @@ def gabriel_graph(
     r"""
     Generate a Gabriel graph from a GeoDataFrame of points.
 
-    In a Gabriel graph two nodes u and v are connected iff the closed disc that has
-    $uv$ as its diameter contains no other node of the set.
+    In a Gabriel graph two nodes u and v are connected iff the open disc that has
+    $uv$ as its diameter contains no other node of the set, i.e. no third node w
+    satisfies $d(u,w)^2 + d(v,w)^2 < d(u,v)^2$.
 
     Parameters
     ----------
@@ -994,15 +995,11 @@ def gabriel_graph(
 
     # Gabriel filtering
     kept_edges = set()
-    tol = 1e-12
     coords = builder.coords
 
     for i, j in delaunay_edges:
-        mid = 0.5 * (coords[i] + coords[j])
-        rad2 = np.sum((coords[i] - coords[j]) ** 2) * 0.25
-        d2 = np.sum((coords - mid) ** 2, axis=1)
-        mask = d2 <= rad2 + tol
-        if np.count_nonzero(mask) == 2:
+        dots = np.einsum("ij,ij->i", coords[i] - coords, coords[j] - coords)
+        if not np.any(dots < 0.0):
             kept_edges.add((builder.node_ids[i], builder.node_ids[j]))
 
     builder.add_edges(kept_edges)
diff --git a/tests/test_proximity.py b/tests/test_proximity.py
index 33eafb6..3267952 100644
--- a/tests/test_proximity.py
+++ b/tests/test_proximity.py
@@ -23,6 +23,7 @@
 
 import geopandas as gpd
 import networkx as nx
+import numpy as np
 import pandas as pd
 import pytest
 from shapely.geometry import LineString
@@ -112,6 +113,41 @@ def test_delaunay_and_subgraphs(small_points: gpd.GeoDataFrame) -> None:
     assert len(r_edges) <= len(d_edges)
 
 
+def test_triangulation_hierarchy_matches_brute_force() -> None:
+    """MST ⊆ RNG ⊆ Gabriel ⊆ Delaunay, and Gabriel matches its brute-force definition.
+
+    Uses large projected-CRS-like coordinates to guard against floating-point
+    regressions in the disc-emptiness predicate (previously valid Gabriel
+    edges were dropped when coordinates were far from the origin).
+    """
+    rng = np.random.default_rng(42)
+    coords = rng.uniform(0.0, 5000.0, size=(150, 2)) + np.array([350_000.0, 5_700_000.0])
+    pts = make_points_simple([(float(x), float(y)) for x, y in coords], crs="EPSG:32633")
+
+    def edge_set(edges: gpd.GeoDataFrame) -> set[tuple[int, int]]:
+        return {(min(int(u), int(v)), max(int(u), int(v))) for u, v in edges.index}
+
+    _, d_edges = delaunay_graph(pts)
+    _, g_edges = gabriel_graph(pts)
+    _, r_edges = relative_neighborhood_graph(pts)
+    _, m_edges = euclidean_minimum_spanning_tree(pts)
+    delaunay, gabriel, rng_graph, mst = map(edge_set, (d_edges, g_edges, r_edges, m_edges))
+
+    # Brute-force Gabriel: keep a Delaunay edge iff no other point lies
+    # strictly inside the open disc having the edge as its diameter.
+    expected_gabriel = set()
+    for i, j in delaunay:
+        mid = 0.5 * (coords[i] + coords[j])
+        rad2 = np.sum((coords[i] - coords[j]) ** 2) * 0.25
+        d2 = np.sum((coords - mid) ** 2, axis=1)
+        d2[[i, j]] = np.inf
+        if not np.any(d2 < rad2):
+            expected_gabriel.add((i, j))
+
+    assert gabriel == expected_gabriel
+    assert mst <= rng_graph <= gabriel <= delaunay
+
+
 def test_mst_and_waxman(small_points: gpd.GeoDataFrame) -> None:
     """MST has n-1 edges and Waxman returns expected schema."""
     _, mst_edges = euclidean_minimum_spanning_tree(small_points)