#!/usr/bin/env python """ ==================== Generators - Classic ==================== Unit tests for various classic graph generators in generators/classic.py """ import itertools import pytest import networkx as nx from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic from networkx.testing import assert_edges_equal from networkx.testing import assert_nodes_equal is_isomorphic = graph_could_be_isomorphic class TestGeneratorClassic(): def test_balanced_tree(self): # balanced_tree(r,h) is a tree with (r**(h+1)-1)/(r-1) edges for r, h in [(2, 2), (3, 3), (6, 2)]: t = nx.balanced_tree(r, h) order = t.order() assert order == (r**(h + 1) - 1) / (r - 1) assert nx.is_connected(t) assert t.size() == order - 1 dh = nx.degree_histogram(t) assert dh[0] == 0 # no nodes of 0 assert dh[1] == r**h # nodes of degree 1 are leaves assert dh[r] == 1 # root is degree r assert dh[r + 1] == order - r**h - 1 # everyone else is degree r+1 assert len(dh) == r + 2 def test_balanced_tree_star(self): # balanced_tree(r,1) is the r-star t = nx.balanced_tree(r=2, h=1) assert is_isomorphic(t, nx.star_graph(2)) t = nx.balanced_tree(r=5, h=1) assert is_isomorphic(t, nx.star_graph(5)) t = nx.balanced_tree(r=10, h=1) assert is_isomorphic(t, nx.star_graph(10)) def test_balanced_tree_path(self): """Tests that the balanced tree with branching factor one is the path graph. """ # A tree of height four has five levels. T = nx.balanced_tree(1, 4) P = nx.path_graph(5) assert is_isomorphic(T, P) def test_full_rary_tree(self): r = 2 n = 9 t = nx.full_rary_tree(r, n) assert t.order() == n assert nx.is_connected(t) dh = nx.degree_histogram(t) assert dh[0] == 0 # no nodes of 0 assert dh[1] == 5 # nodes of degree 1 are leaves assert dh[r] == 1 # root is degree r assert dh[r + 1] == 9 - 5 - 1 # everyone else is degree r+1 assert len(dh) == r + 2 def test_full_rary_tree_balanced(self): t = nx.full_rary_tree(2, 15) th = nx.balanced_tree(2, 3) assert is_isomorphic(t, th) def test_full_rary_tree_path(self): t = nx.full_rary_tree(1, 10) assert is_isomorphic(t, nx.path_graph(10)) def test_full_rary_tree_empty(self): t = nx.full_rary_tree(0, 10) assert is_isomorphic(t, nx.empty_graph(10)) t = nx.full_rary_tree(3, 0) assert is_isomorphic(t, nx.empty_graph(0)) def test_full_rary_tree_3_20(self): t = nx.full_rary_tree(3, 20) assert t.order() == 20 def test_barbell_graph(self): # number of nodes = 2*m1 + m2 (2 m1-complete graphs + m2-path + 2 edges) # number of edges = 2*(nx.number_of_edges(m1-complete graph) + m2 + 1 m1 = 3 m2 = 5 b = nx.barbell_graph(m1, m2) assert nx.number_of_nodes(b) == 2 * m1 + m2 assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1 m1 = 4 m2 = 10 b = nx.barbell_graph(m1, m2) assert nx.number_of_nodes(b) == 2 * m1 + m2 assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1 m1 = 3 m2 = 20 b = nx.barbell_graph(m1, m2) assert nx.number_of_nodes(b) == 2 * m1 + m2 assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1 # Raise NetworkXError if m1<2 m1 = 1 m2 = 20 pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2) # Raise NetworkXError if m2<0 m1 = 5 m2 = -2 pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2) # nx.barbell_graph(2,m) = nx.path_graph(m+4) m1 = 2 m2 = 5 b = nx.barbell_graph(m1, m2) assert is_isomorphic(b, nx.path_graph(m2 + 4)) m1 = 2 m2 = 10 b = nx.barbell_graph(m1, m2) assert is_isomorphic(b, nx.path_graph(m2 + 4)) m1 = 2 m2 = 20 b = nx.barbell_graph(m1, m2) assert is_isomorphic(b, nx.path_graph(m2 + 4)) pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2, create_using=nx.DiGraph()) mb = nx.barbell_graph(m1, m2, create_using=nx.MultiGraph()) assert_edges_equal(mb.edges(), b.edges()) def test_binomial_tree(self): for n in range(0,4): b = nx.binomial_tree(n) assert nx.number_of_nodes(b) == 2**n assert nx.number_of_edges(b) == (2**n - 1) def test_complete_graph(self): # complete_graph(m) is a connected graph with # m nodes and m*(m+1)/2 edges for m in [0, 1, 3, 5]: g = nx.complete_graph(m) assert nx.number_of_nodes(g) == m assert nx.number_of_edges(g) == m * (m - 1) // 2 mg = nx.complete_graph(m, create_using=nx.MultiGraph) assert_edges_equal(mg.edges(), g.edges()) g = nx.complete_graph("abc") assert_nodes_equal(g.nodes(), ['a', 'b', 'c']) assert g.size() == 3 def test_complete_digraph(self): # complete_graph(m) is a connected graph with # m nodes and m*(m+1)/2 edges for m in [0, 1, 3, 5]: g = nx.complete_graph(m, create_using=nx.DiGraph) assert nx.number_of_nodes(g) == m assert nx.number_of_edges(g) == m * (m - 1) g = nx.complete_graph("abc", create_using=nx.DiGraph) assert len(g) == 3 assert g.size() == 6 assert g.is_directed() def test_circular_ladder_graph(self): G = nx.circular_ladder_graph(5) pytest.raises(nx.NetworkXError, nx.circular_ladder_graph, 5, create_using=nx.DiGraph) mG = nx.circular_ladder_graph(5, create_using=nx.MultiGraph) assert_edges_equal(mG.edges(), G.edges()) def test_circulant_graph(self): # Ci_n(1) is the cycle graph for all n Ci6_1 = nx.circulant_graph(6, [1]) C6 = nx.cycle_graph(6) assert_edges_equal(Ci6_1.edges(), C6.edges()) # Ci_n(1, 2, ..., n div 2) is the complete graph for all n Ci7 = nx.circulant_graph(7, [1, 2, 3]) K7 = nx.complete_graph(7) assert_edges_equal(Ci7.edges(), K7.edges()) # Ci_6(1, 3) is K_3,3 i.e. the utility graph Ci6_1_3 = nx.circulant_graph(6, [1, 3]) K3_3 = nx.complete_bipartite_graph(3, 3) assert is_isomorphic(Ci6_1_3, K3_3) def test_cycle_graph(self): G = nx.cycle_graph(4) assert_edges_equal(G.edges(), [(0, 1), (0, 3), (1, 2), (2, 3)]) mG = nx.cycle_graph(4, create_using=nx.MultiGraph) assert_edges_equal(mG.edges(), [(0, 1), (0, 3), (1, 2), (2, 3)]) G = nx.cycle_graph(4, create_using=nx.DiGraph) assert not G.has_edge(2, 1) assert G.has_edge(1, 2) assert G.is_directed() G = nx.cycle_graph("abc") assert len(G) == 3 assert G.size() == 3 g = nx.cycle_graph("abc", nx.DiGraph) assert len(g) == 3 assert g.size() == 3 assert g.is_directed() def test_dorogovtsev_goltsev_mendes_graph(self): G = nx.dorogovtsev_goltsev_mendes_graph(0) assert_edges_equal(G.edges(), [(0, 1)]) assert_nodes_equal(list(G), [0, 1]) G = nx.dorogovtsev_goltsev_mendes_graph(1) assert_edges_equal(G.edges(), [(0, 1), (0, 2), (1, 2)]) assert nx.average_clustering(G) == 1.0 assert sorted(nx.triangles(G).values()) == [1, 1, 1] G = nx.dorogovtsev_goltsev_mendes_graph(10) assert nx.number_of_nodes(G) == 29526 assert nx.number_of_edges(G) == 59049 assert G.degree(0) == 1024 assert G.degree(1) == 1024 assert G.degree(2) == 1024 pytest.raises(nx.NetworkXError, nx.dorogovtsev_goltsev_mendes_graph, 7, create_using=nx.DiGraph) pytest.raises(nx.NetworkXError, nx.dorogovtsev_goltsev_mendes_graph, 7, create_using=nx.MultiGraph) def test_create_using(self): G = nx.empty_graph() assert isinstance(G, nx.Graph) pytest.raises(TypeError, nx.empty_graph, create_using=0.0) pytest.raises(TypeError, nx.empty_graph, create_using="Graph") G = nx.empty_graph(create_using=nx.MultiGraph) assert isinstance(G, nx.MultiGraph) G = nx.empty_graph(create_using=nx.DiGraph) assert isinstance(G, nx.DiGraph) G = nx.empty_graph(create_using=nx.DiGraph, default=nx.MultiGraph) assert isinstance(G, nx.DiGraph) G = nx.empty_graph(create_using=None, default=nx.MultiGraph) assert isinstance(G, nx.MultiGraph) G = nx.empty_graph(default=nx.MultiGraph) assert isinstance(G, nx.MultiGraph) G = nx.path_graph(5) H = nx.empty_graph(create_using=G) assert not H.is_multigraph() assert not H.is_directed() assert len(H) == 0 assert G is H H = nx.empty_graph(create_using=nx.MultiGraph()) assert H.is_multigraph() assert not H.is_directed() assert G is not H def test_empty_graph(self): G = nx.empty_graph() assert nx.number_of_nodes(G) == 0 G = nx.empty_graph(42) assert nx.number_of_nodes(G) == 42 assert nx.number_of_edges(G) == 0 G = nx.empty_graph("abc") assert len(G) == 3 assert G.size() == 0 # create empty digraph G = nx.empty_graph(42, create_using=nx.DiGraph(name="duh")) assert nx.number_of_nodes(G) == 42 assert nx.number_of_edges(G) == 0 assert isinstance(G, nx.DiGraph) # create empty multigraph G = nx.empty_graph(42, create_using=nx.MultiGraph(name="duh")) assert nx.number_of_nodes(G) == 42 assert nx.number_of_edges(G) == 0 assert isinstance(G, nx.MultiGraph) # create empty graph from another pete = nx.petersen_graph() G = nx.empty_graph(42, create_using=pete) assert nx.number_of_nodes(G) == 42 assert nx.number_of_edges(G) == 0 assert isinstance(G, nx.Graph) def test_ladder_graph(self): for i, G in [(0, nx.empty_graph(0)), (1, nx.path_graph(2)), (2, nx.hypercube_graph(2)), (10, nx.grid_graph([2, 10]))]: assert is_isomorphic(nx.ladder_graph(i), G) pytest.raises(nx.NetworkXError, nx.ladder_graph, 2, create_using=nx.DiGraph) g = nx.ladder_graph(2) mg = nx.ladder_graph(2, create_using=nx.MultiGraph) assert_edges_equal(mg.edges(), g.edges()) def test_lollipop_graph(self): # number of nodes = m1 + m2 # number of edges = nx.number_of_edges(nx.complete_graph(m1)) + m2 for m1, m2 in [(3, 5), (4, 10), (3, 20)]: b = nx.lollipop_graph(m1, m2) assert nx.number_of_nodes(b) == m1 + m2 assert nx.number_of_edges(b) == m1 * (m1 - 1) / 2 + m2 # Raise NetworkXError if m<2 pytest.raises(nx.NetworkXError, nx.lollipop_graph, 1, 20) # Raise NetworkXError if n<0 pytest.raises(nx.NetworkXError, nx.lollipop_graph, 5, -2) # lollipop_graph(2,m) = path_graph(m+2) for m1, m2 in [(2, 5), (2, 10), (2, 20)]: b = nx.lollipop_graph(m1, m2) assert is_isomorphic(b, nx.path_graph(m2 + 2)) pytest.raises(nx.NetworkXError, nx.lollipop_graph, m1, m2, create_using=nx.DiGraph) mb = nx.lollipop_graph(m1, m2, create_using=nx.MultiGraph) assert_edges_equal(mb.edges(), b.edges()) g = nx.lollipop_graph([1, 2, 3, 4], "abc") assert len(g) == 7 assert g.size() == 9 def test_null_graph(self): assert nx.number_of_nodes(nx.null_graph()) == 0 def test_path_graph(self): p = nx.path_graph(0) assert is_isomorphic(p, nx.null_graph()) p = nx.path_graph(1) assert is_isomorphic(p, nx.empty_graph(1)) p = nx.path_graph(10) assert nx.is_connected(p) assert (sorted(d for n, d in p.degree()) == [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]) assert p.order() - 1 == p.size() dp = nx.path_graph(3, create_using=nx.DiGraph) assert dp.has_edge(0, 1) assert not dp.has_edge(1, 0) mp = nx.path_graph(10, create_using=nx.MultiGraph) assert_edges_equal(mp.edges(), p.edges()) G = nx.path_graph("abc") assert len(G) == 3 assert G.size() == 2 g = nx.path_graph("abc", nx.DiGraph) assert len(g) == 3 assert g.size() == 2 assert g.is_directed() def test_star_graph(self): star_graph = nx.star_graph assert is_isomorphic(star_graph(0), nx.empty_graph(1)) assert is_isomorphic(star_graph(1), nx.path_graph(2)) assert is_isomorphic(star_graph(2), nx.path_graph(3)) assert is_isomorphic(star_graph(5), nx.complete_bipartite_graph(1, 5)) s = star_graph(10) assert (sorted(d for n, d in s.degree()) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) pytest.raises(nx.NetworkXError, star_graph, 10, create_using=nx.DiGraph) ms = star_graph(10, create_using=nx.MultiGraph) assert_edges_equal(ms.edges(), s.edges()) G = star_graph("abcdefg") assert len(G) == 7 assert G.size() == 6 def test_trivial_graph(self): assert nx.number_of_nodes(nx.trivial_graph()) == 1 def test_turan_graph(self): assert nx.number_of_edges(nx.turan_graph(13, 4)) == 63 assert is_isomorphic(nx.turan_graph(13, 4), nx.complete_multipartite_graph(3, 4, 3, 3)) def test_wheel_graph(self): for n, G in [(0, nx.null_graph()), (1, nx.empty_graph(1)), (2, nx.path_graph(2)), (3, nx.complete_graph(3)), (4, nx.complete_graph(4))]: g = nx.wheel_graph(n) assert is_isomorphic(g, G) g = nx.wheel_graph(10) assert (sorted(d for n, d in g.degree()) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 9]) pytest.raises(nx.NetworkXError, nx.wheel_graph, 10, create_using=nx.DiGraph) mg = nx.wheel_graph(10, create_using=nx.MultiGraph()) assert_edges_equal(mg.edges(), g.edges()) G = nx.wheel_graph("abc") assert len(G) == 3 assert G.size() == 3 def test_complete_0_partite_graph(self): """Tests that the complete 0-partite graph is the null graph.""" G = nx.complete_multipartite_graph() H = nx.null_graph() assert_nodes_equal(G, H) assert_edges_equal(G.edges(), H.edges()) def test_complete_1_partite_graph(self): """Tests that the complete 1-partite graph is the empty graph.""" G = nx.complete_multipartite_graph(3) H = nx.empty_graph(3) assert_nodes_equal(G, H) assert_edges_equal(G.edges(), H.edges()) def test_complete_2_partite_graph(self): """Tests that the complete 2-partite graph is the complete bipartite graph. """ G = nx.complete_multipartite_graph(2, 3) H = nx.complete_bipartite_graph(2, 3) assert_nodes_equal(G, H) assert_edges_equal(G.edges(), H.edges()) def test_complete_multipartite_graph(self): """Tests for generating the complete multipartite graph.""" G = nx.complete_multipartite_graph(2, 3, 4) blocks = [(0, 1), (2, 3, 4), (5, 6, 7, 8)] # Within each block, no two vertices should be adjacent. for block in blocks: for u, v in itertools.combinations_with_replacement(block, 2): assert v not in G[u] assert G.nodes[u] == G.nodes[v] # Across blocks, all vertices should be adjacent. for (block1, block2) in itertools.combinations(blocks, 2): for u, v in itertools.product(block1, block2): assert v in G[u] assert G.nodes[u] != G.nodes[v]