Advance to version 0.1.2

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

docs/source/changelog.rst

@@ -2,6 +2,28 @@ Change Log
 ==========
 
 
+Version 0.1.2
+-------------
+
+Released 2026/3/11
+
+- Fix non-deterministic SPQR decomposition caused by Python hash
+  seed randomization.  ``PathSearcher`` now uses a deterministic
+  DFS start vertex instead of picking from a ``set``.
+
+
+Version 0.1.1
+-------------
+
+Released 2026/3/11
+
+- ``find_triconnected_components()`` now raises ``ValueError`` when
+  the input graph is not biconnected (disconnected or has a cut
+  vertex).  Previously, non-biconnected input was silently accepted
+  and produced incorrect results.
+- Use public API imports in documentation examples.
+
+
 Version 0.1.0
 -------------
 

docs/source/intro.rst

@@ -133,12 +133,11 @@ Using a MultiGraph
 ~~~~~~~~~~~~~~~~~~
 
 For more control, build a
-:class:`~spqrtree._graph.MultiGraph` directly:
+:class:`~spqrtree.MultiGraph` directly:
 
 .. code-block:: python
 
-   from spqrtree._graph import MultiGraph
-   from spqrtree import SPQRTree
+   from spqrtree import MultiGraph, SPQRTree
 
    g = MultiGraph()
    g.add_edge(0, 1)

src/spqrtree/__init__.py

@@ -43,7 +43,7 @@ from spqrtree._triconnected import (
     find_triconnected_components,
 )
 
-VERSION: str = "0.1.0"
+VERSION: str = "0.1.2"
 """The package version."""
 __all__: list[str] = [
     "SPQRTree", "SPQRNode", "NodeType",

src/spqrtree/_triconnected.py

@@ -92,6 +92,41 @@ class TriconnectedComponent:
     """All edges in this component (real and virtual)."""
 
 
+def _check_biconnected(graph: MultiGraph) -> None:
+    """Check that a graph is biconnected (connected with no cut vertex).
+
+    Uses a single DFS pass to verify connectivity and detect cut
+    vertices via Tarjan's algorithm.  A non-root vertex v is a cut
+    vertex if it has a child w such that lowpt1[w] >= dfs_num[v].
+    The DFS root is a cut vertex if it has two or more children.
+
+    :param graph: The multigraph to check.
+    :raises ValueError: If the graph is not connected or has a cut
+        vertex.
+    """
+    start: Hashable = next(iter(graph.vertices))
+    pt: PalmTree = build_palm_tree(graph, start)
+
+    # Check connectivity: DFS must visit all vertices.
+    if len(pt.dfs_num) < graph.num_vertices():
+        raise ValueError("graph is not connected")
+
+    # Check for cut vertices.
+    for v in graph.vertices:
+        if pt.parent[v] is None:
+            # Root: cut vertex if it has 2+ children.
+            if len(pt.children[v]) >= 2:
+                raise ValueError("graph has a cut vertex")
+        else:
+            # Non-root: cut vertex if any child w has
+            # lowpt1[w] >= dfs_num[v].
+            v_num: int = pt.dfs_num[v]
+            for w in pt.children[v]:
+                if pt.lowpt1[w] >= v_num:
+                    raise ValueError(
+                        "graph has a cut vertex")
+
+
 def find_triconnected_components(
     graph: MultiGraph,
 ) -> list[TriconnectedComponent]:
@@ -108,10 +143,14 @@ def find_triconnected_components(
 
     :param graph: A biconnected multigraph.
     :return: A list of TriconnectedComponent objects.
+    :raises ValueError: If the graph is not connected or has a
+        cut vertex.
     """
     if graph.num_vertices() == 0 or graph.num_edges() == 0:
         return []
 
+    _check_biconnected(graph)
+
     # Work on a copy to avoid modifying the caller's graph.
     g: MultiGraph = graph.copy()
 
@@ -379,7 +418,11 @@ class _PathSearcher:
         """Set of virtual edge IDs."""
 
         # Build palm tree and sort adjacency lists.
-        start: Hashable = next(iter(g.vertices))
+        # Use the first remaining edge's endpoint as start vertex
+        # for deterministic DFS ordering.  Edge IDs are sequential
+        # integers, so g.edges[0] is always the lowest-ID edge,
+        # regardless of Python hash seed.
+        start: Hashable = g.edges[0].u
         pt: PalmTree = build_palm_tree(g, start)
         sort_adjacency_lists(g, pt)
         pt = build_palm_tree(g, start)

tests/test_graph.py

@@ -20,7 +20,7 @@
 import unittest
 from collections.abc import Hashable
 
-from spqrtree._graph import Edge, MultiGraph
+from spqrtree import Edge, MultiGraph
 
 
 class TestEdge(unittest.TestCase):

tests/test_palm_tree.py

@@ -24,7 +24,7 @@ DFS from vertex 1.  Edge insertion order is specified in each test.
 import unittest
 from collections.abc import Hashable
 
-from spqrtree._graph import Edge, MultiGraph
+from spqrtree import Edge, MultiGraph
 from spqrtree._palm_tree import PalmTree, build_palm_tree, phi_key
 
 

tests/test_spqrtree.py

@@ -21,13 +21,21 @@
 Tests cover: triangle K3 (S-node), K4 (R-node), C4 (S-node),
 two parallel edges (Q-node), and three parallel edges (P-node).
 """
+import os
+import subprocess
+import sys
 import time
 import unittest
 from collections import deque
 from collections.abc import Hashable
 
-from spqrtree._graph import Edge, MultiGraph
-from spqrtree._spqr import NodeType, SPQRNode, build_spqr_tree
+from spqrtree import (
+    Edge,
+    MultiGraph,
+    NodeType,
+    SPQRNode,
+    build_spqr_tree,
+)
 
 
 def _make_k3() -> MultiGraph:
@@ -2795,6 +2803,44 @@ class TestSPQRWikimediaSpqr(unittest.TestCase):
         )
         self.assertEqual(n, 1)
 
+    def test_s_node_vertices(self) -> None:
+        """Test that the S-node has vertices {g, h, l, m}."""
+        s_nodes: list[SPQRNode] = [
+            nd for nd in self.all_nodes
+            if nd.type == NodeType.S
+        ]
+        self.assertEqual(len(s_nodes), 1)
+        self.assertEqual(
+            set(s_nodes[0].skeleton.vertices),
+            {'g', 'h', 'l', 'm'},
+        )
+
+    def test_p_node_vertices(self) -> None:
+        """Test that the P-node has vertices {l, m}."""
+        p_nodes: list[SPQRNode] = [
+            nd for nd in self.all_nodes
+            if nd.type == NodeType.P
+        ]
+        self.assertEqual(len(p_nodes), 1)
+        self.assertEqual(
+            set(p_nodes[0].skeleton.vertices),
+            {'l', 'm'},
+        )
+
+    def test_r_node_vertex_sets(self) -> None:
+        """Test exact vertex sets of R-nodes."""
+        r_verts: list[frozenset[Hashable]] = [
+            frozenset(nd.skeleton.vertices)
+            for nd in self.all_nodes
+            if nd.type == NodeType.R
+        ]
+        expected: set[frozenset[Hashable]] = {
+            frozenset({'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h'}),
+            frozenset({'h', 'i', 'j', 'k', 'm', 'n'}),
+            frozenset({'l', 'm', 'o', 'p'}),
+        }
+        self.assertEqual(set(r_verts), expected)
+
     def test_no_adjacent_s_nodes(self) -> None:
         """Test that no S-node is adjacent to another S-node."""
         _assert_no_ss_pp(self, self.root, NodeType.S)
@@ -2851,3 +2897,112 @@ class TestSPQRRpstFig1a(unittest.TestCase):
     def test_no_adjacent_p_nodes(self) -> None:
         """Test that no P-node is adjacent to another P-node."""
         _assert_no_ss_pp(self, self.root, NodeType.P)
+
+
+class TestBuildSpqrTreeBiconnectivity(unittest.TestCase):
+    """Tests that build_spqr_tree rejects non-biconnected graphs."""
+
+    def test_cut_vertex_raises(self) -> None:
+        """Test that a graph with a cut vertex raises ValueError."""
+        g: MultiGraph = MultiGraph()
+        g.add_edge(1, 2)
+        g.add_edge(2, 3)
+        g.add_edge(1, 3)
+        g.add_edge(3, 4)
+        g.add_edge(4, 5)
+        g.add_edge(3, 5)
+        with self.assertRaises(ValueError) as ctx:
+            build_spqr_tree(g)
+        self.assertIn("cut vertex", str(ctx.exception))
+
+    def test_disconnected_raises(self) -> None:
+        """Test that a disconnected graph raises ValueError."""
+        g: MultiGraph = MultiGraph()
+        g.add_edge(1, 2)
+        g.add_edge(3, 4)
+        with self.assertRaises(ValueError) as ctx:
+            build_spqr_tree(g)
+        self.assertIn("not connected", str(ctx.exception))
+
+    def test_path_raises(self) -> None:
+        """Test that a path graph raises ValueError."""
+        g: MultiGraph = MultiGraph()
+        g.add_edge(1, 2)
+        g.add_edge(2, 3)
+        with self.assertRaises(ValueError) as ctx:
+            build_spqr_tree(g)
+        self.assertIn("cut vertex", str(ctx.exception))
+
+
+# Script used by TestSPQRTreeDeterminism to run SPQR-tree
+# construction in a subprocess with a specific PYTHONHASHSEED.
+_SUBPROCESS_SCRIPT: str = """
+import json, sys
+from collections import deque
+sys.path.insert(0, "src")
+from spqrtree import MultiGraph, NodeType, SPQRNode, build_spqr_tree
+
+g = MultiGraph()
+edges = [
+    ('a', 'b'), ('a', 'c'), ('a', 'g'),
+    ('b', 'd'), ('b', 'h'), ('c', 'd'),
+    ('c', 'e'), ('d', 'f'), ('e', 'f'),
+    ('e', 'g'), ('f', 'h'), ('h', 'i'),
+    ('h', 'j'), ('i', 'j'), ('i', 'n'),
+    ('j', 'k'), ('k', 'm'), ('k', 'n'),
+    ('m', 'n'), ('l', 'm'), ('l', 'o'),
+    ('l', 'p'), ('m', 'o'), ('m', 'p'),
+    ('o', 'p'), ('g', 'l'),
+]
+for u, v in edges:
+    g.add_edge(u, v)
+root = build_spqr_tree(g)
+nodes = []
+queue = deque([root])
+while queue:
+    nd = queue.popleft()
+    verts = sorted(nd.skeleton.vertices)
+    nodes.append({"type": nd.type.value, "vertices": verts})
+    for ch in nd.children:
+        queue.append(ch)
+nodes.sort(key=lambda x: (x["type"], x["vertices"]))
+print(json.dumps(nodes))
+"""
+
+
+class TestSPQRTreeDeterminism(unittest.TestCase):
+    """Test that SPQR-tree construction is deterministic.
+
+    Runs SPQR-tree construction of the Wikimedia SPQR example
+    graph in subprocesses with different PYTHONHASHSEED values
+    and verifies that all runs produce identical results.
+    """
+
+    def test_deterministic_across_hash_seeds(self) -> None:
+        """Test consistent results with 20 different hash seeds."""
+        results: list[str] = []
+        env: dict[str, str] = os.environ.copy()
+        cwd: str = os.path.join(
+            os.path.dirname(__file__), os.pardir
+        )
+        for seed in range(20):
+            env["PYTHONHASHSEED"] = str(seed)
+            proc: subprocess.CompletedProcess[str] = \
+                subprocess.run(
+                    [sys.executable, "-c", _SUBPROCESS_SCRIPT],
+                    capture_output=True, text=True,
+                    env=env, cwd=cwd,
+                )
+            self.assertEqual(
+                proc.returncode, 0,
+                f"seed={seed} failed:\n{proc.stderr}"
+            )
+            results.append(proc.stdout.strip())
+        # All runs must produce the same result.
+        for i, r in enumerate(results):
+            self.assertEqual(
+                r, results[0],
+                f"seed={i} differs from seed=0:\n"
+                f"  seed=0: {results[0]}\n"
+                f"  seed={i}: {r}"
+            )

tests/test_triconnected.py

@@ -22,12 +22,16 @@ Tests cover: triangle K3, 4-cycle C4, complete graph K4, two parallel
 edges, three parallel edges, real-edge count invariant, and virtual
 edge appearance count.
 """
+import os
+import subprocess
+import sys
 import unittest
 from collections.abc import Hashable
 
-from spqrtree._graph import Edge, MultiGraph
-from spqrtree._triconnected import (
+from spqrtree import (
     ComponentType,
+    Edge,
+    MultiGraph,
     TriconnectedComponent,
     find_triconnected_components,
 )
@@ -2740,6 +2744,49 @@ class TestTriconnectedWikimediaSpqr(unittest.TestCase):
         )
         self.assertEqual(n, 1)
 
+    def test_polygon_vertices(self) -> None:
+        """Test that the POLYGON has vertices {g, h, l, m}."""
+        polygons: list[TriconnectedComponent] = [
+            c for c in self.comps
+            if c.type == ComponentType.POLYGON
+        ]
+        self.assertEqual(len(polygons), 1)
+        verts: set[Hashable] = set()
+        for e in polygons[0].edges:
+            verts.add(e.u)
+            verts.add(e.v)
+        self.assertEqual(verts, {'g', 'h', 'l', 'm'})
+
+    def test_bond_vertices(self) -> None:
+        """Test that the BOND has vertices {l, m}."""
+        bonds: list[TriconnectedComponent] = [
+            c for c in self.comps
+            if c.type == ComponentType.BOND
+        ]
+        self.assertEqual(len(bonds), 1)
+        verts: set[Hashable] = set()
+        for e in bonds[0].edges:
+            verts.add(e.u)
+            verts.add(e.v)
+        self.assertEqual(verts, {'l', 'm'})
+
+    def test_triconnected_vertex_sets(self) -> None:
+        """Test exact vertex sets of TRICONNECTED components."""
+        tri_verts: list[frozenset[Hashable]] = []
+        for c in self.comps:
+            if c.type == ComponentType.TRICONNECTED:
+                verts: set[Hashable] = set()
+                for e in c.edges:
+                    verts.add(e.u)
+                    verts.add(e.v)
+                tri_verts.append(frozenset(verts))
+        expected: set[frozenset[Hashable]] = {
+            frozenset({'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h'}),
+            frozenset({'h', 'i', 'j', 'k', 'm', 'n'}),
+            frozenset({'l', 'm', 'o', 'p'}),
+        }
+        self.assertEqual(set(tri_verts), expected)
+
     def test_all_invariants(self) -> None:
         """Test all decomposition invariants."""
         _check_all_invariants(self, self.g, self.comps)
@@ -2785,3 +2832,158 @@ class TestTriconnectedRpstFig1a(unittest.TestCase):
     def test_all_invariants(self) -> None:
         """Test all decomposition invariants."""
         _check_all_invariants(self, self.g, self.comps)
+
+
+def _make_cut_vertex_graph() -> MultiGraph:
+    """Build a graph with a cut vertex.
+
+    Graph: 1-2-3 triangle connected to 3-4-5 triangle via
+    shared vertex 3 (the cut vertex).
+
+    :return: A MultiGraph with a cut vertex at vertex 3.
+    """
+    g: MultiGraph = MultiGraph()
+    g.add_edge(1, 2)
+    g.add_edge(2, 3)
+    g.add_edge(1, 3)
+    g.add_edge(3, 4)
+    g.add_edge(4, 5)
+    g.add_edge(3, 5)
+    return g
+
+
+def _make_disconnected_graph() -> MultiGraph:
+    """Build a disconnected graph with two components.
+
+    Component 1: edge 1-2.
+    Component 2: edge 3-4.
+
+    :return: A disconnected MultiGraph.
+    """
+    g: MultiGraph = MultiGraph()
+    g.add_edge(1, 2)
+    g.add_edge(3, 4)
+    return g
+
+
+def _make_path_graph() -> MultiGraph:
+    """Build a path graph 1-2-3 (not biconnected).
+
+    Vertex 2 is a cut vertex (removing it disconnects 1 and 3).
+
+    :return: A MultiGraph representing a path.
+    """
+    g: MultiGraph = MultiGraph()
+    g.add_edge(1, 2)
+    g.add_edge(2, 3)
+    return g
+
+
+class TestBiconnectivityCheck(unittest.TestCase):
+    """Tests that non-biconnected graphs raise ValueError."""
+
+    def test_cut_vertex_raises(self) -> None:
+        """Test that a graph with a cut vertex raises ValueError."""
+        g: MultiGraph = _make_cut_vertex_graph()
+        with self.assertRaises(ValueError) as ctx:
+            find_triconnected_components(g)
+        self.assertIn("cut vertex", str(ctx.exception))
+
+    def test_disconnected_raises(self) -> None:
+        """Test that a disconnected graph raises ValueError."""
+        g: MultiGraph = _make_disconnected_graph()
+        with self.assertRaises(ValueError) as ctx:
+            find_triconnected_components(g)
+        self.assertIn("not connected", str(ctx.exception))
+
+    def test_path_raises(self) -> None:
+        """Test that a path graph (has cut vertex) raises ValueError."""
+        g: MultiGraph = _make_path_graph()
+        with self.assertRaises(ValueError) as ctx:
+            find_triconnected_components(g)
+        self.assertIn("cut vertex", str(ctx.exception))
+
+    def test_single_vertex_no_edges(self) -> None:
+        """Test that a single vertex with no edges returns empty."""
+        g: MultiGraph = MultiGraph()
+        g.add_vertex(1)
+        comps: list[TriconnectedComponent] = \
+            find_triconnected_components(g)
+        self.assertEqual(comps, [])
+
+    def test_biconnected_graph_ok(self) -> None:
+        """Test that a biconnected graph does not raise."""
+        g: MultiGraph = _make_k3()
+        comps: list[TriconnectedComponent] = \
+            find_triconnected_components(g)
+        self.assertEqual(len(comps), 1)
+
+
+# Script used by TestTriconnectedDeterminism to run decomposition
+# in a subprocess with a specific PYTHONHASHSEED.
+_SUBPROCESS_SCRIPT: str = """
+import json, sys
+sys.path.insert(0, "src")
+from spqrtree import (
+    ComponentType, MultiGraph, find_triconnected_components,
+)
+
+g = MultiGraph()
+edges = [
+    ('a', 'b'), ('a', 'c'), ('a', 'g'),
+    ('b', 'd'), ('b', 'h'), ('c', 'd'),
+    ('c', 'e'), ('d', 'f'), ('e', 'f'),
+    ('e', 'g'), ('f', 'h'), ('h', 'i'),
+    ('h', 'j'), ('i', 'j'), ('i', 'n'),
+    ('j', 'k'), ('k', 'm'), ('k', 'n'),
+    ('m', 'n'), ('l', 'm'), ('l', 'o'),
+    ('l', 'p'), ('m', 'o'), ('m', 'p'),
+    ('o', 'p'), ('g', 'l'),
+]
+for u, v in edges:
+    g.add_edge(u, v)
+comps = find_triconnected_components(g)
+result = []
+for c in comps:
+    verts = sorted({ep for e in c.edges for ep in (e.u, e.v)})
+    result.append({"type": c.type.value, "vertices": verts})
+result.sort(key=lambda x: (x["type"], x["vertices"]))
+print(json.dumps(result))
+"""
+
+
+class TestTriconnectedDeterminism(unittest.TestCase):
+    """Test that triconnected decomposition is deterministic.
+
+    Runs decomposition of the Wikimedia SPQR example graph in
+    subprocesses with different PYTHONHASHSEED values and verifies
+    that all runs produce identical results.
+    """
+
+    def test_deterministic_across_hash_seeds(self) -> None:
+        """Test consistent results with 20 different hash seeds."""
+        results: list[str] = []
+        env: dict[str, str] = os.environ.copy()
+        for seed in range(20):
+            env["PYTHONHASHSEED"] = str(seed)
+            proc: subprocess.CompletedProcess[str] = \
+                subprocess.run(
+                    [sys.executable, "-c", _SUBPROCESS_SCRIPT],
+                    capture_output=True, text=True, env=env,
+                    cwd=os.path.join(
+                        os.path.dirname(__file__), os.pardir
+                    ),
+                )
+            self.assertEqual(
+                proc.returncode, 0,
+                f"seed={seed} failed:\n{proc.stderr}"
+            )
+            results.append(proc.stdout.strip())
+        # All runs must produce the same result.
+        for i, r in enumerate(results):
+            self.assertEqual(
+                r, results[0],
+                f"seed={i} differs from seed=0:\n"
+                f"  seed=0: {results[0]}\n"
+                f"  seed={i}: {r}"
+            )