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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/tests/test_treewidth.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/tests/test_treewidth.py
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+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/tests/test_treewidth.py
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+import itertools
+
+import networkx as nx
+from networkx.algorithms.approximation import (
+    treewidth_min_degree,
+    treewidth_min_fill_in,
+)
+from networkx.algorithms.approximation.treewidth import (
+    MinDegreeHeuristic,
+    min_fill_in_heuristic,
+)
+
+
+def is_tree_decomp(graph, decomp):
+    """Check if the given tree decomposition is valid."""
+    for x in graph.nodes():
+        appear_once = False
+        for bag in decomp.nodes():
+            if x in bag:
+                appear_once = True
+                break
+        assert appear_once
+
+    # Check if each connected pair of nodes are at least once together in a bag
+    for x, y in graph.edges():
+        appear_together = False
+        for bag in decomp.nodes():
+            if x in bag and y in bag:
+                appear_together = True
+                break
+        assert appear_together
+
+    # Check if the nodes associated with vertex v form a connected subset of T
+    for v in graph.nodes():
+        subset = []
+        for bag in decomp.nodes():
+            if v in bag:
+                subset.append(bag)
+        sub_graph = decomp.subgraph(subset)
+        assert nx.is_connected(sub_graph)
+
+
+class TestTreewidthMinDegree:
+    """Unit tests for the min_degree function"""
+
+    @classmethod
+    def setup_class(cls):
+        """Setup for different kinds of trees"""
+        cls.complete = nx.Graph()
+        cls.complete.add_edge(1, 2)
+        cls.complete.add_edge(2, 3)
+        cls.complete.add_edge(1, 3)
+
+        cls.small_tree = nx.Graph()
+        cls.small_tree.add_edge(1, 3)
+        cls.small_tree.add_edge(4, 3)
+        cls.small_tree.add_edge(2, 3)
+        cls.small_tree.add_edge(3, 5)
+        cls.small_tree.add_edge(5, 6)
+        cls.small_tree.add_edge(5, 7)
+        cls.small_tree.add_edge(6, 7)
+
+        cls.deterministic_graph = nx.Graph()
+        cls.deterministic_graph.add_edge(0, 1)  # deg(0) = 1
+
+        cls.deterministic_graph.add_edge(1, 2)  # deg(1) = 2
+
+        cls.deterministic_graph.add_edge(2, 3)
+        cls.deterministic_graph.add_edge(2, 4)  # deg(2) = 3
+
+        cls.deterministic_graph.add_edge(3, 4)
+        cls.deterministic_graph.add_edge(3, 5)
+        cls.deterministic_graph.add_edge(3, 6)  # deg(3) = 4
+
+        cls.deterministic_graph.add_edge(4, 5)
+        cls.deterministic_graph.add_edge(4, 6)
+        cls.deterministic_graph.add_edge(4, 7)  # deg(4) = 5
+
+        cls.deterministic_graph.add_edge(5, 6)
+        cls.deterministic_graph.add_edge(5, 7)
+        cls.deterministic_graph.add_edge(5, 8)
+        cls.deterministic_graph.add_edge(5, 9)  # deg(5) = 6
+
+        cls.deterministic_graph.add_edge(6, 7)
+        cls.deterministic_graph.add_edge(6, 8)
+        cls.deterministic_graph.add_edge(6, 9)  # deg(6) = 6
+
+        cls.deterministic_graph.add_edge(7, 8)
+        cls.deterministic_graph.add_edge(7, 9)  # deg(7) = 5
+
+        cls.deterministic_graph.add_edge(8, 9)  # deg(8) = 4
+
+    def test_petersen_graph(self):
+        """Test Petersen graph tree decomposition result"""
+        G = nx.petersen_graph()
+        _, decomp = treewidth_min_degree(G)
+        is_tree_decomp(G, decomp)
+
+    def test_small_tree_treewidth(self):
+        """Test small tree
+
+        Test if the computed treewidth of the known self.small_tree is 2.
+        As we know which value we can expect from our heuristic, values other
+        than two are regressions
+        """
+        G = self.small_tree
+        # the order of removal should be [1,2,4]3[5,6,7]
+        # (with [] denoting any order of the containing nodes)
+        # resulting in treewidth 2 for the heuristic
+        treewidth, _ = treewidth_min_fill_in(G)
+        assert treewidth == 2
+
+    def test_heuristic_abort(self):
+        """Test heuristic abort condition for fully connected graph"""
+        graph = {}
+        for u in self.complete:
+            graph[u] = set()
+            for v in self.complete[u]:
+                if u != v:  # ignore self-loop
+                    graph[u].add(v)
+
+        deg_heuristic = MinDegreeHeuristic(graph)
+        node = deg_heuristic.best_node(graph)
+        if node is None:
+            pass
+        else:
+            assert False
+
+    def test_empty_graph(self):
+        """Test empty graph"""
+        G = nx.Graph()
+        _, _ = treewidth_min_degree(G)
+
+    def test_two_component_graph(self):
+        G = nx.Graph()
+        G.add_node(1)
+        G.add_node(2)
+        treewidth, _ = treewidth_min_degree(G)
+        assert treewidth == 0
+
+    def test_not_sortable_nodes(self):
+        G = nx.Graph([(0, "a")])
+        treewidth_min_degree(G)
+
+    def test_heuristic_first_steps(self):
+        """Test first steps of min_degree heuristic"""
+        graph = {
+            n: set(self.deterministic_graph[n]) - {n} for n in self.deterministic_graph
+        }
+        deg_heuristic = MinDegreeHeuristic(graph)
+        elim_node = deg_heuristic.best_node(graph)
+        print(f"Graph {graph}:")
+        steps = []
+
+        while elim_node is not None:
+            print(f"Removing {elim_node}:")
+            steps.append(elim_node)
+            nbrs = graph[elim_node]
+
+            for u, v in itertools.permutations(nbrs, 2):
+                if v not in graph[u]:
+                    graph[u].add(v)
+
+            for u in graph:
+                if elim_node in graph[u]:
+                    graph[u].remove(elim_node)
+
+            del graph[elim_node]
+            print(f"Graph {graph}:")
+            elim_node = deg_heuristic.best_node(graph)
+
+        # check only the first 5 elements for equality
+        assert steps[:5] == [0, 1, 2, 3, 4]
+
+
+class TestTreewidthMinFillIn:
+    """Unit tests for the treewidth_min_fill_in function."""
+
+    @classmethod
+    def setup_class(cls):
+        """Setup for different kinds of trees"""
+        cls.complete = nx.Graph()
+        cls.complete.add_edge(1, 2)
+        cls.complete.add_edge(2, 3)
+        cls.complete.add_edge(1, 3)
+
+        cls.small_tree = nx.Graph()
+        cls.small_tree.add_edge(1, 2)
+        cls.small_tree.add_edge(2, 3)
+        cls.small_tree.add_edge(3, 4)
+        cls.small_tree.add_edge(1, 4)
+        cls.small_tree.add_edge(2, 4)
+        cls.small_tree.add_edge(4, 5)
+        cls.small_tree.add_edge(5, 6)
+        cls.small_tree.add_edge(5, 7)
+        cls.small_tree.add_edge(6, 7)
+
+        cls.deterministic_graph = nx.Graph()
+        cls.deterministic_graph.add_edge(1, 2)
+        cls.deterministic_graph.add_edge(1, 3)
+        cls.deterministic_graph.add_edge(3, 4)
+        cls.deterministic_graph.add_edge(2, 4)
+        cls.deterministic_graph.add_edge(3, 5)
+        cls.deterministic_graph.add_edge(4, 5)
+        cls.deterministic_graph.add_edge(3, 6)
+        cls.deterministic_graph.add_edge(5, 6)
+
+    def test_petersen_graph(self):
+        """Test Petersen graph tree decomposition result"""
+        G = nx.petersen_graph()
+        _, decomp = treewidth_min_fill_in(G)
+        is_tree_decomp(G, decomp)
+
+    def test_small_tree_treewidth(self):
+        """Test if the computed treewidth of the known self.small_tree is 2"""
+        G = self.small_tree
+        # the order of removal should be [1,2,4]3[5,6,7]
+        # (with [] denoting any order of the containing nodes)
+        # resulting in treewidth 2 for the heuristic
+        treewidth, _ = treewidth_min_fill_in(G)
+        assert treewidth == 2
+
+    def test_heuristic_abort(self):
+        """Test if min_fill_in returns None for fully connected graph"""
+        graph = {}
+        for u in self.complete:
+            graph[u] = set()
+            for v in self.complete[u]:
+                if u != v:  # ignore self-loop
+                    graph[u].add(v)
+        next_node = min_fill_in_heuristic(graph)
+        if next_node is None:
+            pass
+        else:
+            assert False
+
+    def test_empty_graph(self):
+        """Test empty graph"""
+        G = nx.Graph()
+        _, _ = treewidth_min_fill_in(G)
+
+    def test_two_component_graph(self):
+        G = nx.Graph()
+        G.add_node(1)
+        G.add_node(2)
+        treewidth, _ = treewidth_min_fill_in(G)
+        assert treewidth == 0
+
+    def test_not_sortable_nodes(self):
+        G = nx.Graph([(0, "a")])
+        treewidth_min_fill_in(G)
+
+    def test_heuristic_first_steps(self):
+        """Test first steps of min_fill_in heuristic"""
+        graph = {
+            n: set(self.deterministic_graph[n]) - {n} for n in self.deterministic_graph
+        }
+        print(f"Graph {graph}:")
+        elim_node = min_fill_in_heuristic(graph)
+        steps = []
+
+        while elim_node is not None:
+            print(f"Removing {elim_node}:")
+            steps.append(elim_node)
+            nbrs = graph[elim_node]
+
+            for u, v in itertools.permutations(nbrs, 2):
+                if v not in graph[u]:
+                    graph[u].add(v)
+
+            for u in graph:
+                if elim_node in graph[u]:
+                    graph[u].remove(elim_node)
+
+            del graph[elim_node]
+            print(f"Graph {graph}:")
+            elim_node = min_fill_in_heuristic(graph)
+
+        # check only the first 2 elements for equality
+        assert steps[:2] == [6, 5]