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+"""Tests for the :mod:`networkx.algorithms.triads` module."""
+
+import itertools
+from collections import defaultdict
+from random import sample
+
+import pytest
+
+import networkx as nx
+
+
+def test_all_triplets_deprecated():
+    G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+    with pytest.deprecated_call():
+        nx.all_triplets(G)
+
+
+def test_random_triad_deprecated():
+    G = nx.path_graph(3, create_using=nx.DiGraph)
+    with pytest.deprecated_call():
+        nx.random_triad(G)
+
+
+def test_triadic_census():
+    """Tests the triadic_census function."""
+    G = nx.DiGraph()
+    G.add_edges_from(["01", "02", "03", "04", "05", "12", "16", "51", "56", "65"])
+    expected = {
+        "030T": 2,
+        "120C": 1,
+        "210": 0,
+        "120U": 0,
+        "012": 9,
+        "102": 3,
+        "021U": 0,
+        "111U": 0,
+        "003": 8,
+        "030C": 0,
+        "021D": 9,
+        "201": 0,
+        "111D": 1,
+        "300": 0,
+        "120D": 0,
+        "021C": 2,
+    }
+    actual = nx.triadic_census(G)
+    assert expected == actual
+
+
+def test_is_triad():
+    """Tests the is_triad function"""
+    G = nx.karate_club_graph()
+    G = G.to_directed()
+    for i in range(100):
+        nodes = sample(sorted(G.nodes()), 3)
+        G2 = G.subgraph(nodes)
+        assert nx.is_triad(G2)
+
+
+def test_all_triplets():
+    """Tests the all_triplets function."""
+    G = nx.DiGraph()
+    G.add_edges_from(["01", "02", "03", "04", "05", "12", "16", "51", "56", "65"])
+    expected = [
+        f"{i},{j},{k}"
+        for i in range(7)
+        for j in range(i + 1, 7)
+        for k in range(j + 1, 7)
+    ]
+    expected = [set(x.split(",")) for x in expected]
+    actual = [set(x) for x in nx.all_triplets(G)]
+    assert all(any(s1 == s2 for s1 in expected) for s2 in actual)
+
+
+def test_all_triads():
+    """Tests the all_triplets function."""
+    G = nx.DiGraph()
+    G.add_edges_from(["01", "02", "03", "04", "05", "12", "16", "51", "56", "65"])
+    expected = [
+        f"{i},{j},{k}"
+        for i in range(7)
+        for j in range(i + 1, 7)
+        for k in range(j + 1, 7)
+    ]
+    expected = [G.subgraph(x.split(",")) for x in expected]
+    actual = list(nx.all_triads(G))
+    assert all(any(nx.is_isomorphic(G1, G2) for G1 in expected) for G2 in actual)
+
+
+def test_triad_type():
+    """Tests the triad_type function."""
+    # 0 edges (1 type)
+    G = nx.DiGraph({0: [], 1: [], 2: []})
+    assert nx.triad_type(G) == "003"
+    # 1 edge (1 type)
+    G = nx.DiGraph({0: [1], 1: [], 2: []})
+    assert nx.triad_type(G) == "012"
+    # 2 edges (4 types)
+    G = nx.DiGraph([(0, 1), (0, 2)])
+    assert nx.triad_type(G) == "021D"
+    G = nx.DiGraph({0: [1], 1: [0], 2: []})
+    assert nx.triad_type(G) == "102"
+    G = nx.DiGraph([(0, 1), (2, 1)])
+    assert nx.triad_type(G) == "021U"
+    G = nx.DiGraph([(0, 1), (1, 2)])
+    assert nx.triad_type(G) == "021C"
+    # 3 edges (4 types)
+    G = nx.DiGraph([(0, 1), (1, 0), (2, 1)])
+    assert nx.triad_type(G) == "111D"
+    G = nx.DiGraph([(0, 1), (1, 0), (1, 2)])
+    assert nx.triad_type(G) == "111U"
+    G = nx.DiGraph([(0, 1), (1, 2), (0, 2)])
+    assert nx.triad_type(G) == "030T"
+    G = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
+    assert nx.triad_type(G) == "030C"
+    # 4 edges (4 types)
+    G = nx.DiGraph([(0, 1), (1, 0), (2, 0), (0, 2)])
+    assert nx.triad_type(G) == "201"
+    G = nx.DiGraph([(0, 1), (1, 0), (2, 0), (2, 1)])
+    assert nx.triad_type(G) == "120D"
+    G = nx.DiGraph([(0, 1), (1, 0), (0, 2), (1, 2)])
+    assert nx.triad_type(G) == "120U"
+    G = nx.DiGraph([(0, 1), (1, 0), (0, 2), (2, 1)])
+    assert nx.triad_type(G) == "120C"
+    # 5 edges (1 type)
+    G = nx.DiGraph([(0, 1), (1, 0), (2, 1), (1, 2), (0, 2)])
+    assert nx.triad_type(G) == "210"
+    # 6 edges (1 type)
+    G = nx.DiGraph([(0, 1), (1, 0), (1, 2), (2, 1), (0, 2), (2, 0)])
+    assert nx.triad_type(G) == "300"
+
+
+def test_triads_by_type():
+    """Tests the all_triplets function."""
+    G = nx.DiGraph()
+    G.add_edges_from(["01", "02", "03", "04", "05", "12", "16", "51", "56", "65"])
+    all_triads = nx.all_triads(G)
+    expected = defaultdict(list)
+    for triad in all_triads:
+        name = nx.triad_type(triad)
+        expected[name].append(triad)
+    actual = nx.triads_by_type(G)
+    assert set(actual.keys()) == set(expected.keys())
+    for tri_type, actual_Gs in actual.items():
+        expected_Gs = expected[tri_type]
+        for a in actual_Gs:
+            assert any(nx.is_isomorphic(a, e) for e in expected_Gs)
+
+
+def test_random_triad():
+    """Tests the random_triad function"""
+    G = nx.karate_club_graph()
+    G = G.to_directed()
+    for i in range(100):
+        assert nx.is_triad(nx.random_triad(G))
+
+    G = nx.DiGraph()
+    msg = "at least 3 nodes to form a triad"
+    with pytest.raises(nx.NetworkXError, match=msg):
+        nx.random_triad(G)
+
+
+def test_triadic_census_short_path_nodelist():
+    G = nx.path_graph("abc", create_using=nx.DiGraph)
+    expected = {"021C": 1}
+    for nl in ["a", "b", "c", "ab", "ac", "bc", "abc"]:
+        triad_census = nx.triadic_census(G, nodelist=nl)
+        assert expected == {typ: cnt for typ, cnt in triad_census.items() if cnt > 0}
+
+
+def test_triadic_census_correct_nodelist_values():
+    G = nx.path_graph(5, create_using=nx.DiGraph)
+    msg = r"nodelist includes duplicate nodes or nodes not in G"
+    with pytest.raises(ValueError, match=msg):
+        nx.triadic_census(G, [1, 2, 2, 3])
+    with pytest.raises(ValueError, match=msg):
+        nx.triadic_census(G, [1, 2, "a", 3])
+
+
+def test_triadic_census_tiny_graphs():
+    tc = nx.triadic_census(nx.empty_graph(0, create_using=nx.DiGraph))
+    assert {} == {typ: cnt for typ, cnt in tc.items() if cnt > 0}
+    tc = nx.triadic_census(nx.empty_graph(1, create_using=nx.DiGraph))
+    assert {} == {typ: cnt for typ, cnt in tc.items() if cnt > 0}
+    tc = nx.triadic_census(nx.empty_graph(2, create_using=nx.DiGraph))
+    assert {} == {typ: cnt for typ, cnt in tc.items() if cnt > 0}
+    tc = nx.triadic_census(nx.DiGraph([(1, 2)]))
+    assert {} == {typ: cnt for typ, cnt in tc.items() if cnt > 0}
+
+
+def test_triadic_census_selfloops():
+    GG = nx.path_graph("abc", create_using=nx.DiGraph)
+    expected = {"021C": 1}
+    for n in GG:
+        G = GG.copy()
+        G.add_edge(n, n)
+        tc = nx.triadic_census(G)
+        assert expected == {typ: cnt for typ, cnt in tc.items() if cnt > 0}
+
+    GG = nx.path_graph("abcde", create_using=nx.DiGraph)
+    tbt = nx.triads_by_type(GG)
+    for n in GG:
+        GG.add_edge(n, n)
+    tc = nx.triadic_census(GG)
+    assert tc == {tt: len(tbt[tt]) for tt in tc}
+
+
+def test_triadic_census_four_path():
+    G = nx.path_graph("abcd", create_using=nx.DiGraph)
+    expected = {"012": 2, "021C": 2}
+    triad_census = nx.triadic_census(G)
+    assert expected == {typ: cnt for typ, cnt in triad_census.items() if cnt > 0}
+
+
+def test_triadic_census_four_path_nodelist():
+    G = nx.path_graph("abcd", create_using=nx.DiGraph)
+    expected_end = {"012": 2, "021C": 1}
+    expected_mid = {"012": 1, "021C": 2}
+    a_triad_census = nx.triadic_census(G, nodelist=["a"])
+    assert expected_end == {typ: cnt for typ, cnt in a_triad_census.items() if cnt > 0}
+    b_triad_census = nx.triadic_census(G, nodelist=["b"])
+    assert expected_mid == {typ: cnt for typ, cnt in b_triad_census.items() if cnt > 0}
+    c_triad_census = nx.triadic_census(G, nodelist=["c"])
+    assert expected_mid == {typ: cnt for typ, cnt in c_triad_census.items() if cnt > 0}
+    d_triad_census = nx.triadic_census(G, nodelist=["d"])
+    assert expected_end == {typ: cnt for typ, cnt in d_triad_census.items() if cnt > 0}
+
+
+def test_triadic_census_nodelist():
+    """Tests the triadic_census function."""
+    G = nx.DiGraph()
+    G.add_edges_from(["01", "02", "03", "04", "05", "12", "16", "51", "56", "65"])
+    expected = {
+        "030T": 2,
+        "120C": 1,
+        "210": 0,
+        "120U": 0,
+        "012": 9,
+        "102": 3,
+        "021U": 0,
+        "111U": 0,
+        "003": 8,
+        "030C": 0,
+        "021D": 9,
+        "201": 0,
+        "111D": 1,
+        "300": 0,
+        "120D": 0,
+        "021C": 2,
+    }
+    actual = {k: 0 for k in expected}
+    for node in G.nodes():
+        node_triad_census = nx.triadic_census(G, nodelist=[node])
+        for triad_key in expected:
+            actual[triad_key] += node_triad_census[triad_key]
+    # Divide all counts by 3
+    for k, v in actual.items():
+        actual[k] //= 3
+    assert expected == actual
+
+
+@pytest.mark.parametrize("N", [5, 10])
+def test_triadic_census_on_random_graph(N):
+    G = nx.binomial_graph(N, 0.3, directed=True, seed=42)
+    tc1 = nx.triadic_census(G)
+    tbt = nx.triads_by_type(G)
+    tc2 = {tt: len(tbt[tt]) for tt in tc1}
+    assert tc1 == tc2
+
+    for n in G:
+        tc1 = nx.triadic_census(G, nodelist={n})
+        tc2 = {tt: sum(1 for t in tbt.get(tt, []) if n in t) for tt in tc1}
+        assert tc1 == tc2
+
+    for ns in itertools.combinations(G, 2):
+        ns = set(ns)
+        tc1 = nx.triadic_census(G, nodelist=ns)
+        tc2 = {
+            tt: sum(1 for t in tbt.get(tt, []) if any(n in ns for n in t)) for tt in tc1
+        }
+        assert tc1 == tc2
+
+    for ns in itertools.combinations(G, 3):
+        ns = set(ns)
+        tc1 = nx.triadic_census(G, nodelist=ns)
+        tc2 = {
+            tt: sum(1 for t in tbt.get(tt, []) if any(n in ns for n in t)) for tt in tc1
+        }
+        assert tc1 == tc2