diff --git a/README.md b/README.md
index 61913c41..7b7f0dd0 100644
--- a/README.md
+++ b/README.md
@@ -85,7 +85,7 @@ Graphs belong to the class `UGraph` or `DGraph` for undirected or directed graph
 
     ***
 - `g.adjacency()` adjacency matrix
-- `g.Laplacian()` Laplacian matrix
+- `g.laplacian()` Laplacian matrix
 - `g.incidence()` incidence matrix
 
 ### Properties and methods of a vertex
diff --git a/docs/source/matrices.rst b/docs/source/matrices.rst
index dcf9d3d6..d323b756 100644
--- a/docs/source/matrices.rst
+++ b/docs/source/matrices.rst
@@ -4,4 +4,4 @@ Convert graph to matrix form
 These methods convert a graph to a matrix representation .
 
 .. autoclass:: pgraph.PGraph._BaseGraph
-    :members: distance, adjacency, degree, incidence, Laplacian
+    :members: distance, adjacency, degree, incidence, laplacian
diff --git a/src/pgraph/PGraph.py b/src/pgraph/PGraph.py
index d44b815a..61efcdf3 100644
--- a/src/pgraph/PGraph.py
+++ b/src/pgraph/PGraph.py
@@ -1966,14 +1966,14 @@ def average_degree(self) -> float:
 
     # MATRIX REPRESENTATIONS
 
-    def Laplacian(self) -> NDArray:
+    def laplacian(self) -> NDArray:
         """
         Laplacian matrix for the graph
 
         :return: Laplacian matrix
         :rtype: NumPy ndarray
 
-        ``g.Laplacian()`` is the Laplacian matrix (NxN) of the graph where N
+        ``g.laplacian()`` is the Laplacian matrix (NxN) of the graph where N
         is the number of vertices.
 
         .. runblock:: pycon
@@ -1987,7 +1987,7 @@ def Laplacian(self) -> NDArray:
             >>> for i, j in [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (3, 4)]:
             ...     g.add_edge(g[i], g[j])
             ...
-            >>> L = g.Laplacian()
+            >>> L = g.laplacian()
             >>> print(L)
 
         .. note::
@@ -2023,6 +2023,24 @@ def Laplacian(self) -> NDArray:
         """
         return np.diag([v.out_degree for v in self]) - self.adjacency()
 
+    def Laplacian(self) -> NDArray:
+        """
+        Laplacian matrix for the graph (deprecated)
+
+        .. deprecated:: 1.0
+            Use :meth:`laplacian` instead.  A capitalized name denotes a class
+            method that constructs a graph, like :meth:`Adjacency` and
+            :meth:`Dict`; this is an instance method that returns a matrix.
+
+        :seealso: :meth:`laplacian`
+        """
+        warnings.warn(
+            "Laplacian() is deprecated, use laplacian() instead",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        return self.laplacian()
+
     def connectivity(self, vertices: Iterable[BaseVertex] | None = None) -> list[int]:
         """
         Graph connectivity
@@ -2094,7 +2112,7 @@ def degree(self) -> NDArray:
             For a ``DGraph`` this was the out-degree matrix, counting only the
             edges leaving each vertex.  It is now the total, in plus out.  The
             old matrix is ``np.diag([v.out_degree for v in g])``, which is what
-            :meth:`Laplacian` uses.
+            :meth:`laplacian` uses.
 
         .. runblock:: pycon
 
@@ -2116,7 +2134,7 @@ def degree(self) -> NDArray:
         add ``k`` to the degree of each end.  A self-loop adds 2, for both
         kinds of graph, since it has two ends.
 
-        :seealso: :meth:`adjacency` :meth:`incidence` :meth:`Laplacian`
+        :seealso: :meth:`adjacency` :meth:`incidence` :meth:`laplacian`
             :meth:`connectivity` :meth:`average_degree` :attr:`BaseVertex.degree`
         """
 
@@ -2166,7 +2184,7 @@ def adjacency(self) -> NDArray:
         (consistent with :meth:`degree`) and 1 for a ``DGraph``. In every case
         each row of ``A`` sums to the degree of that vertex.
 
-        :seealso: :meth:`Laplacian` :meth:`incidence` :meth:`degree`
+        :seealso: :meth:`laplacian` :meth:`incidence` :meth:`degree`
         """
         # create a dict mapping vertex to an id
         vdict = {}
@@ -2222,7 +2240,7 @@ def incidence(self) -> NDArray:
         so row sums still equal :meth:`degree`); for a ``DGraph`` it holds a
         single 1.
 
-        :seealso: :meth:`Laplacian` :meth:`adjacency` :meth:`degree`
+        :seealso: :meth:`laplacian` :meth:`adjacency` :meth:`degree`
         """
         edges = self.edges()
         I = np.zeros((self.n, len(edges)))
diff --git a/tests/test_graph.py b/tests/test_graph.py
index 94fc4f34..8003a0b5 100644
--- a/tests/test_graph.py
+++ b/tests/test_graph.py
@@ -588,7 +588,7 @@ def test_matrices(self):
         D = g.degree()
         nt.assert_array_equal(D, np.diag([2, 1, 1, 0]))
 
-        L = g.Laplacian()
+        L = g.laplacian()
         expected_L = np.diag([2, 1, 1, 0]) - expected_A
         nt.assert_array_equal(L, expected_L)
 
@@ -902,7 +902,7 @@ def test_matrices(self):
 
         # the directed Laplacian uses the OUT-degree, D_out - A, whose rows
         # sum to zero; it is not degree() - A for a directed graph
-        L = g.Laplacian()
+        L = g.laplacian()
         expected_L = np.diag([2, 1, 0]) - expected_A
         nt.assert_array_equal(L, expected_L)
         nt.assert_array_equal(L.sum(axis=1), np.zeros(3))
diff --git a/tests/test_in_edges.py b/tests/test_in_edges.py
index 3ae807ff..7f9be411 100644
--- a/tests/test_in_edges.py
+++ b/tests/test_in_edges.py
@@ -65,7 +65,7 @@ def test_average_degree(self):
 
     def test_laplacian_still_has_zero_row_sums(self):
         # a directed Laplacian uses the OUT-degree: D_out - A
-        L = self.g.Laplacian()
+        L = self.g.laplacian()
         np.testing.assert_allclose(L.sum(axis=1), 0)
         np.testing.assert_array_equal(
             L, np.diag([v.out_degree for v in self.g]) - self.g.adjacency()
diff --git a/tests/test_laplacian_name.py b/tests/test_laplacian_name.py
new file mode 100644
index 00000000..f605f243
--- /dev/null
+++ b/tests/test_laplacian_name.py
@@ -0,0 +1,43 @@
+"""``laplacian()`` is canonical; ``Laplacian()`` is a deprecated alias."""
+
+import unittest
+import warnings
+
+import numpy as np
+
+from pgraph import DGraph, UGraph
+
+
+class _Name:
+    cls: type
+
+    def setUp(self):
+        self.g = self.cls()
+        a, b, c = (self.g.add_vertex() for _ in range(3))
+        self.g.add_edge(a, b)
+        self.g.add_edge(b, c)
+
+    def test_lowercase_does_not_warn(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")
+            L = self.g.laplacian()
+        self.assertEqual(L.shape, (3, 3))
+
+    def test_capitalized_warns_and_agrees(self):
+        with self.assertWarns(DeprecationWarning) as cm:
+            L = self.g.Laplacian()
+        self.assertIn("laplacian()", str(cm.warning))
+        self.assertEqual(cm.filename, __file__)  # stacklevel points at caller
+        np.testing.assert_array_equal(L, self.g.laplacian())
+
+
+class TestUGraphName(_Name, unittest.TestCase):
+    cls = UGraph
+
+
+class TestDGraphName(_Name, unittest.TestCase):
+    cls = DGraph
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_multigraph.py b/tests/test_multigraph.py
index c1883d2a..9199dec7 100644
--- a/tests/test_multigraph.py
+++ b/tests/test_multigraph.py
@@ -19,7 +19,7 @@
   towards the (out-)degree of a ``DGraph`` vertex
 - ``adjacency()`` counts edges, so ``A[i, j]`` is the number of edges
   from ``i`` to ``j`` and each row of ``A`` sums to the degree of the vertex
-- ``Laplacian()`` is therefore ``degree() - adjacency()``, rows sum to zero
+- ``laplacian()`` is therefore ``degree() - adjacency()``, rows sum to zero
 - ``distance()`` and path lengths use the cheapest of any parallel edges
 """
 
@@ -118,7 +118,7 @@ def check_matrices_consistent(self):
             np.testing.assert_array_equal(out, deg)
 
         # the Laplacian is D_out - A, so each row sums to zero for any graph
-        L = g.Laplacian()
+        L = g.laplacian()
         np.testing.assert_array_equal(L, np.diag(out) - A)
         np.testing.assert_allclose(L.sum(axis=1), 0)
         # and degrees sum to twice the edges (every edge has two ends)