"""Unit tests for the :mod:`networkx.generators.random_graphs` module.""" import pytest import networkx as nx _gnp_generators = [ nx.gnp_random_graph, nx.fast_gnp_random_graph, nx.binomial_graph, nx.erdos_renyi_graph, ] @pytest.mark.parametrize("generator", _gnp_generators) @pytest.mark.parametrize("directed", (True, False)) def test_gnp_generators_negative_edge_probability(generator, directed): """If the edge probability `p` is <=0, the resulting graph should have no edges.""" G = generator(10, -1.1, directed=directed) assert len(G) == 10 assert G.number_of_edges() == 0 assert G.is_directed() == directed @pytest.mark.parametrize("generator", _gnp_generators) @pytest.mark.parametrize( ("directed", "expected_num_edges"), [(False, 45), (True, 90)], ) def test_gnp_generators_greater_than_1_edge_probability( generator, directed, expected_num_edges ): """If the edge probability `p` is >=1, the resulting graph should be complete.""" G = generator(10, 1.1, directed=directed) assert len(G) == 10 assert G.number_of_edges() == expected_num_edges assert G.is_directed() == directed @pytest.mark.parametrize("generator", _gnp_generators) @pytest.mark.parametrize("directed", (True, False)) def test_gnp_generators_basic(generator, directed): """If the edge probability `p` is >0 and <1, test only the basic properties.""" G = generator(10, 0.1, directed=directed) assert len(G) == 10 assert G.is_directed() == directed @pytest.mark.parametrize("generator", _gnp_generators) def test_gnp_generators_for_p_close_to_1(generator): """If the edge probability `p` is close to 1, the resulting graph should have all edges.""" runs = 100 edges = sum( generator(10, 0.99999, directed=True).number_of_edges() for _ in range(runs) ) assert abs(edges / float(runs) - 90) <= runs * 2.0 / 100 @pytest.mark.parametrize("generator", _gnp_generators) @pytest.mark.parametrize("p", (0.2, 0.8)) @pytest.mark.parametrize("directed", (True, False)) def test_gnp_generators_edge_probability(generator, p, directed): """Test that gnp generators generate edges according to the their probability `p`.""" runs = 5000 n = 5 edge_counts = [[0] * n for _ in range(n)] for i in range(runs): G = generator(n, p, directed=directed) for v, w in G.edges: edge_counts[v][w] += 1 if not directed: edge_counts[w][v] += 1 for v in range(n): for w in range(n): if v == w: # There should be no loops assert edge_counts[v][w] == 0 else: # Each edge should have been generated with probability close to p assert abs(edge_counts[v][w] / float(runs) - p) <= 0.03 @pytest.mark.parametrize( "generator", [nx.gnp_random_graph, nx.binomial_graph, nx.erdos_renyi_graph] ) @pytest.mark.parametrize( ("seed", "directed", "expected_num_edges"), [(42, False, 1219), (42, True, 2454), (314, False, 1247), (314, True, 2476)], ) def test_gnp_random_graph_aliases(generator, seed, directed, expected_num_edges): """Test that aliases give the same result with the same seed.""" G = generator(100, 0.25, seed=seed, directed=directed) assert len(G) == 100 assert G.number_of_edges() == expected_num_edges assert G.is_directed() == directed class TestGeneratorsRandom: def test_random_graph(self): seed = 42 G = nx.gnm_random_graph(100, 20, seed) G = nx.gnm_random_graph(100, 20, seed, directed=True) G = nx.dense_gnm_random_graph(100, 20, seed) G = nx.barabasi_albert_graph(100, 1, seed) G = nx.barabasi_albert_graph(100, 3, seed) assert G.number_of_edges() == (97 * 3) G = nx.barabasi_albert_graph(100, 3, seed, nx.complete_graph(5)) assert G.number_of_edges() == (10 + 95 * 3) G = nx.extended_barabasi_albert_graph(100, 1, 0, 0, seed) assert G.number_of_edges() == 99 G = nx.extended_barabasi_albert_graph(100, 3, 0, 0, seed) assert G.number_of_edges() == 97 * 3 G = nx.extended_barabasi_albert_graph(100, 1, 0, 0.5, seed) assert G.number_of_edges() == 99 G = nx.extended_barabasi_albert_graph(100, 2, 0.5, 0, seed) assert G.number_of_edges() > 100 * 3 assert G.number_of_edges() < 100 * 4 G = nx.extended_barabasi_albert_graph(100, 2, 0.3, 0.3, seed) assert G.number_of_edges() > 100 * 2 assert G.number_of_edges() < 100 * 4 G = nx.powerlaw_cluster_graph(100, 1, 1.0, seed) G = nx.powerlaw_cluster_graph(100, 3, 0.0, seed) assert G.number_of_edges() == (97 * 3) G = nx.random_regular_graph(10, 20, seed) pytest.raises(nx.NetworkXError, nx.random_regular_graph, 3, 21) pytest.raises(nx.NetworkXError, nx.random_regular_graph, 33, 21) constructor = [(10, 20, 0.8), (20, 40, 0.8)] G = nx.random_shell_graph(constructor, seed) def is_caterpillar(g): """ A tree is a caterpillar iff all nodes of degree >=3 are surrounded by at most two nodes of degree two or greater. ref: http://mathworld.wolfram.com/CaterpillarGraph.html """ deg_over_3 = [n for n in g if g.degree(n) >= 3] for n in deg_over_3: nbh_deg_over_2 = [nbh for nbh in g.neighbors(n) if g.degree(nbh) >= 2] if not len(nbh_deg_over_2) <= 2: return False return True def is_lobster(g): """ A tree is a lobster if it has the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007) ref: http://mathworld.wolfram.com/LobsterGraph.html """ non_leafs = [n for n in g if g.degree(n) > 1] return is_caterpillar(g.subgraph(non_leafs)) G = nx.random_lobster(10, 0.1, 0.5, seed) assert max(G.degree(n) for n in G.nodes()) > 3 assert is_lobster(G) pytest.raises(nx.NetworkXError, nx.random_lobster, 10, 0.1, 1, seed) pytest.raises(nx.NetworkXError, nx.random_lobster, 10, 1, 1, seed) pytest.raises(nx.NetworkXError, nx.random_lobster, 10, 1, 0.5, seed) # docstring says this should be a caterpillar G = nx.random_lobster(10, 0.1, 0.0, seed) assert is_caterpillar(G) # difficult to find seed that requires few tries seq = nx.random_powerlaw_tree_sequence(10, 3, seed=14, tries=1) G = nx.random_powerlaw_tree(10, 3, seed=14, tries=1) def test_dual_barabasi_albert(self, m1=1, m2=4, p=0.5): """ Tests that the dual BA random graph generated behaves consistently. Tests the exceptions are raised as expected. The graphs generation are repeated several times to prevent lucky shots """ seeds = [42, 314, 2718] initial_graph = nx.complete_graph(10) for seed in seeds: # This should be BA with m = m1 BA1 = nx.barabasi_albert_graph(100, m1, seed) DBA1 = nx.dual_barabasi_albert_graph(100, m1, m2, 1, seed) assert BA1.edges() == DBA1.edges() # This should be BA with m = m2 BA2 = nx.barabasi_albert_graph(100, m2, seed) DBA2 = nx.dual_barabasi_albert_graph(100, m1, m2, 0, seed) assert BA2.edges() == DBA2.edges() BA3 = nx.barabasi_albert_graph(100, m1, seed) DBA3 = nx.dual_barabasi_albert_graph(100, m1, m1, p, seed) # We can't compare edges here since randomness is "consumed" when drawing # between m1 and m2 assert BA3.size() == DBA3.size() DBA = nx.dual_barabasi_albert_graph(100, m1, m2, p, seed, initial_graph) BA1 = nx.barabasi_albert_graph(100, m1, seed, initial_graph) BA2 = nx.barabasi_albert_graph(100, m2, seed, initial_graph) assert ( min(BA1.size(), BA2.size()) <= DBA.size() <= max(BA1.size(), BA2.size()) ) # Testing exceptions dbag = nx.dual_barabasi_albert_graph pytest.raises(nx.NetworkXError, dbag, m1, m1, m2, 0) pytest.raises(nx.NetworkXError, dbag, m2, m1, m2, 0) pytest.raises(nx.NetworkXError, dbag, 100, m1, m2, -0.5) pytest.raises(nx.NetworkXError, dbag, 100, m1, m2, 1.5) initial = nx.complete_graph(max(m1, m2) - 1) pytest.raises(nx.NetworkXError, dbag, 100, m1, m2, p, initial_graph=initial) def test_extended_barabasi_albert(self, m=2): """ Tests that the extended BA random graph generated behaves consistently. Tests the exceptions are raised as expected. The graphs generation are repeated several times to prevent lucky-shots """ seeds = [42, 314, 2718] for seed in seeds: BA_model = nx.barabasi_albert_graph(100, m, seed) BA_model_edges = BA_model.number_of_edges() # This behaves just like BA, the number of edges must be the same G1 = nx.extended_barabasi_albert_graph(100, m, 0, 0, seed) assert G1.size() == BA_model_edges # More than twice more edges should have been added G1 = nx.extended_barabasi_albert_graph(100, m, 0.8, 0, seed) assert G1.size() > BA_model_edges * 2 # Only edge rewiring, so the number of edges less than original G2 = nx.extended_barabasi_albert_graph(100, m, 0, 0.8, seed) assert G2.size() == BA_model_edges # Mixed scenario: less edges than G1 and more edges than G2 G3 = nx.extended_barabasi_albert_graph(100, m, 0.3, 0.3, seed) assert G3.size() > G2.size() assert G3.size() < G1.size() # Testing exceptions ebag = nx.extended_barabasi_albert_graph pytest.raises(nx.NetworkXError, ebag, m, m, 0, 0) pytest.raises(nx.NetworkXError, ebag, 1, 0.5, 0, 0) pytest.raises(nx.NetworkXError, ebag, 100, 2, 0.5, 0.5) def test_random_zero_regular_graph(self): """Tests that a 0-regular graph has the correct number of nodes and edges. """ seed = 42 G = nx.random_regular_graph(0, 10, seed) assert len(G) == 10 assert G.number_of_edges() == 0 def test_gnm(self): G = nx.gnm_random_graph(10, 3) assert len(G) == 10 assert G.number_of_edges() == 3 G = nx.gnm_random_graph(10, 3, seed=42) assert len(G) == 10 assert G.number_of_edges() == 3 G = nx.gnm_random_graph(10, 100) assert len(G) == 10 assert G.number_of_edges() == 45 G = nx.gnm_random_graph(10, 100, directed=True) assert len(G) == 10 assert G.number_of_edges() == 90 G = nx.gnm_random_graph(10, -1.1) assert len(G) == 10 assert G.number_of_edges() == 0 def test_watts_strogatz_big_k(self): # Test to make sure than n <= k pytest.raises(nx.NetworkXError, nx.watts_strogatz_graph, 10, 11, 0.25) pytest.raises(nx.NetworkXError, nx.newman_watts_strogatz_graph, 10, 11, 0.25) # could create an infinite loop, now doesn't # infinite loop used to occur when a node has degree n-1 and needs to rewire nx.watts_strogatz_graph(10, 9, 0.25, seed=0) nx.newman_watts_strogatz_graph(10, 9, 0.5, seed=0) # Test k==n scenario nx.watts_strogatz_graph(10, 10, 0.25, seed=0) nx.newman_watts_strogatz_graph(10, 10, 0.25, seed=0) def test_random_kernel_graph(self): def integral(u, w, z): return c * (z - w) def root(u, w, r): return r / c + w c = 1 graph = nx.random_kernel_graph(1000, integral, root) graph = nx.random_kernel_graph(1000, integral, root, seed=42) assert len(graph) == 1000 @pytest.mark.parametrize( ("k", "expected_num_nodes", "expected_num_edges"), [ (2, 10, 10), (4, 10, 20), ], ) def test_watts_strogatz(k, expected_num_nodes, expected_num_edges): G = nx.watts_strogatz_graph(10, k, 0.25, seed=42) assert len(G) == expected_num_nodes assert G.number_of_edges() == expected_num_edges def test_newman_watts_strogatz_zero_probability(): G = nx.newman_watts_strogatz_graph(10, 2, 0.0, seed=42) assert len(G) == 10 assert G.number_of_edges() == 10 def test_newman_watts_strogatz_nonzero_probability(): G = nx.newman_watts_strogatz_graph(10, 4, 0.25, seed=42) assert len(G) == 10 assert G.number_of_edges() >= 20 def test_connected_watts_strogatz(): G = nx.connected_watts_strogatz_graph(10, 2, 0.1, tries=10, seed=42) assert len(G) == 10 assert G.number_of_edges() == 10 def test_connected_watts_strogatz_zero_tries(): with pytest.raises(nx.NetworkXError, match="Maximum number of tries exceeded"): nx.connected_watts_strogatz_graph(10, 2, 0.1, tries=0) @pytest.mark.parametrize( "generator, kwargs", [ (nx.fast_gnp_random_graph, {"n": 20, "p": 0.2, "directed": False}), (nx.fast_gnp_random_graph, {"n": 20, "p": 0.2, "directed": True}), (nx.gnp_random_graph, {"n": 20, "p": 0.2, "directed": False}), (nx.gnp_random_graph, {"n": 20, "p": 0.2, "directed": True}), (nx.dense_gnm_random_graph, {"n": 30, "m": 4}), (nx.gnm_random_graph, {"n": 30, "m": 4, "directed": False}), (nx.gnm_random_graph, {"n": 30, "m": 4, "directed": True}), (nx.newman_watts_strogatz_graph, {"n": 50, "k": 5, "p": 0.1}), (nx.watts_strogatz_graph, {"n": 50, "k": 5, "p": 0.1}), (nx.connected_watts_strogatz_graph, {"n": 50, "k": 5, "p": 0.1}), (nx.random_regular_graph, {"d": 5, "n": 20}), (nx.barabasi_albert_graph, {"n": 40, "m": 3}), (nx.dual_barabasi_albert_graph, {"n": 40, "m1": 3, "m2": 2, "p": 0.1}), (nx.extended_barabasi_albert_graph, {"n": 40, "m": 3, "p": 0.1, "q": 0.2}), (nx.powerlaw_cluster_graph, {"n": 40, "m": 3, "p": 0.1}), (nx.random_lobster, {"n": 40, "p1": 0.1, "p2": 0.2}), (nx.random_shell_graph, {"constructor": [(10, 20, 0.8), (20, 40, 0.8)]}), (nx.random_powerlaw_tree, {"n": 10, "seed": 14, "tries": 1}), ( nx.random_kernel_graph, { "n": 10, "kernel_integral": lambda u, w, z: z - w, "kernel_root": lambda u, w, r: r + w, }, ), ], ) @pytest.mark.parametrize("create_using_instance", [False, True]) def test_create_using(generator, kwargs, create_using_instance): class DummyGraph(nx.Graph): pass class DummyDiGraph(nx.DiGraph): pass create_using_type = DummyDiGraph if kwargs.get("directed") else DummyGraph create_using = create_using_type() if create_using_instance else create_using_type graph = generator(**kwargs, create_using=create_using) assert isinstance(graph, create_using_type) @pytest.mark.parametrize("directed", [True, False]) @pytest.mark.parametrize("fn", (nx.fast_gnp_random_graph, nx.gnp_random_graph)) def test_gnp_fns_disallow_multigraph(fn, directed): with pytest.raises(nx.NetworkXError, match="must not be a multi-graph"): fn(20, 0.2, create_using=nx.MultiGraph) @pytest.mark.parametrize("fn", (nx.gnm_random_graph, nx.dense_gnm_random_graph)) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_gnm_fns_disallow_directed_and_multigraph(fn, graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): fn(10, 20, create_using=graphtype) @pytest.mark.parametrize( "fn", ( nx.newman_watts_strogatz_graph, nx.watts_strogatz_graph, nx.connected_watts_strogatz_graph, ), ) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_watts_strogatz_disallow_directed_and_multigraph(fn, graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): fn(10, 2, 0.2, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_random_regular_graph_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.random_regular_graph(2, 10, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_barabasi_albert_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.barabasi_albert_graph(10, 3, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_dual_barabasi_albert_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.dual_barabasi_albert_graph(10, 2, 1, 0.4, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_extended_barabasi_albert_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.extended_barabasi_albert_graph(10, 2, 0.2, 0.3, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_powerlaw_cluster_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.powerlaw_cluster_graph(10, 5, 0.2, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_random_lobster_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.random_lobster(10, 0.1, 0.1, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_random_shell_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.random_shell_graph([(10, 20, 2), (10, 20, 5)], create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_random_powerlaw_tree_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.random_powerlaw_tree(10, create_using=graphtype) @pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)) def test_random_kernel_disallow_directed_and_multigraph(graphtype): with pytest.raises(nx.NetworkXError, match="must not be"): nx.random_kernel_graph( 10, lambda y, a, b: a + b, lambda u, w, r: r + w, create_using=graphtype )