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