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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
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