diff --git a/CHANGES b/CHANGES
index 886411295..290d98be5 100644
--- a/CHANGES
+++ b/CHANGES
@@ -17,6 +17,7 @@ Pint Changelog
 - Add conductivity dimension. (#2112)
 - Add absorbance unit and dimension. (#2114)
 - Add membrane filtration flux and permeability dimensionality, and shorthand "LMH". (#2116)
+- Fix find_shortest_path to use breadth first search (#2146)
 
 
 0.24.4 (2024-11-07)
diff --git a/pint/testsuite/test_util.py b/pint/testsuite/test_util.py
index 0a6d357d0..3eb49a471 100644
--- a/pint/testsuite/test_util.py
+++ b/pint/testsuite/test_util.py
@@ -304,6 +304,21 @@ def test_shortest_path(self):
         p = find_shortest_path(g, 2, 1)
         assert p == [2, 1]
 
+    def test_shortest_path_densely_connected_2146(self):
+        import itertools
+        g = collections.defaultdict(set)
+        for i, j in itertools.combinations(range(42), 2):
+            g[i].add(j)
+            g[j].add(i)
+        p = find_shortest_path(g, 0, 39)
+        assert p == [0, 39]
+        p = find_shortest_path(g, 0, 41)
+        assert p == [0, 41]
+        p = find_shortest_path(g, 17, 2)
+        assert p == [17, 2]
+        p = find_shortest_path(g, 12, 12)
+        assert p == [12]
+
 
 class TestMatrix:
     def test_matrix_to_string(self):
diff --git a/pint/util.py b/pint/util.py
index b10ba6d3a..fe3ab43db 100644
--- a/pint/util.py
+++ b/pint/util.py
@@ -16,6 +16,7 @@
 import re
 import tokenize
 import types
+from collections import deque
 from collections.abc import Callable, Generator, Hashable, Iterable, Iterator, Mapping
 from fractions import Fraction
 from functools import lru_cache, partial
@@ -340,7 +341,7 @@ def solve_dependencies(
 
 
 def find_shortest_path(
-    graph: dict[TH, set[TH]], start: TH, end: TH, path: list[TH] | None = None
+    graph: dict[TH, set[TH]], start: TH, end: TH
 ):
     """Find shortest path between two nodes within a graph.
 
@@ -353,32 +354,29 @@ def find_shortest_path(
         Starting node.
     end
         End node.
-    path
-        Path to prepend to the one found.
-        (default = None, empty path.)
 
     Returns
     -------
     list[TH]
         The shortest path between two nodes.
     """
-    path = (path or []) + [start]
+    path = [start]
     if start == end:
         return path
 
-    # TODO: raise ValueError when start not in graph
-    if start not in graph:
-        return None
-
-    shortest = None
-    for node in graph[start]:
-        if node not in path:
-            newpath = find_shortest_path(graph, node, end, path)
-            if newpath:
-                if not shortest or len(newpath) < len(shortest):
-                    shortest = newpath
+    fifo = deque()
+    fifo.append((start, path))
+    visited = set()
+    while fifo:
+        node, path = fifo.popleft()
+        visited.add(node)
+        for adjascent_node in graph[node] - visited:
+            if adjascent_node == end:
+                return path + [adjascent_node]
+            else:
+                fifo.append((adjascent_node, path + [adjascent_node]))
 
-    return shortest
+    return None
 
 
 def find_connected_nodes(