342 lines
12 KiB
Python
342 lines
12 KiB
Python
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import pytest
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import networkx as nx
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from networkx.algorithms.planarity import get_counterexample
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from networkx.algorithms.planarity import get_counterexample_recursive
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from networkx.algorithms.planarity import check_planarity_recursive
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class TestLRPlanarity:
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"""Nose Unit tests for the :mod:`networkx.algorithms.planarity` module.
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Tests three things:
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1. Check that the result is correct
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(returns planar if and only if the graph is actually planar)
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2. In case a counter example is returned: Check if it is correct
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3. In case an embedding is returned: Check if its actually an embedding
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"""
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@staticmethod
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def check_graph(G, is_planar=None):
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"""Raises an exception if the lr_planarity check returns a wrong result
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Parameters
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----------
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G : NetworkX graph
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is_planar : bool
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The expected result of the planarity check.
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If set to None only counter example or embedding are verified.
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"""
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# obtain results of planarity check
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is_planar_lr, result = nx.check_planarity(G, True)
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is_planar_lr_rec, result_rec = check_planarity_recursive(G, True)
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if is_planar is not None:
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# set a message for the assert
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if is_planar:
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msg = "Wrong planarity check result. Should be planar."
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else:
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msg = "Wrong planarity check result. Should be non-planar."
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# check if the result is as expected
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assert is_planar == is_planar_lr, msg
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assert is_planar == is_planar_lr_rec, msg
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if is_planar_lr:
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# check embedding
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check_embedding(G, result)
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check_embedding(G, result_rec)
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else:
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# check counter example
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check_counterexample(G, result)
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check_counterexample(G, result_rec)
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def test_simple_planar_graph(self):
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e = [(1, 2), (2, 3), (3, 4), (4, 6), (6, 7), (7, 1), (1, 5),
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(5, 2), (2, 4), (4, 5), (5, 7)]
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self.check_graph(nx.Graph(e), is_planar=True)
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def test_planar_with_selfloop(self):
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e = [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 2), (1, 3),
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(1, 5), (2, 5), (2, 4), (3, 4), (3, 5), (4, 5)]
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self.check_graph(nx.Graph(e), is_planar=True)
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def test_k3_3(self):
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self.check_graph(nx.complete_bipartite_graph(3, 3), is_planar=False)
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def test_k5(self):
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self.check_graph(nx.complete_graph(5), is_planar=False)
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def test_multiple_components_planar(self):
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e = [(1, 2), (2, 3), (3, 1), (4, 5), (5, 6), (6, 4)]
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self.check_graph(nx.Graph(e), is_planar=True)
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def test_multiple_components_non_planar(self):
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G = nx.complete_graph(5)
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# add another planar component to the non planar component
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# G stays non planar
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G.add_edges_from([(6, 7), (7, 8), (8, 6)])
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self.check_graph(G, is_planar=False)
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def test_non_planar_with_selfloop(self):
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G = nx.complete_graph(5)
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# add self loops
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for i in range(5):
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G.add_edge(i, i)
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self.check_graph(G, is_planar=False)
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def test_non_planar1(self):
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# tests a graph that has no subgraph directly isomorph to K5 or K3_3
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e = [(1, 5), (1, 6), (1, 7), (2, 6), (2, 3), (3, 5), (3, 7), (4, 5),
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(4, 6), (4, 7)]
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self.check_graph(nx.Graph(e), is_planar=False)
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def test_loop(self):
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# test a graph with a selfloop
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e = [(1, 2), (2, 2)]
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G = nx.Graph(e)
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self.check_graph(G, is_planar=True)
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def test_comp(self):
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# test multiple component graph
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e = [(1, 2), (3, 4)]
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G = nx.Graph(e)
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G.remove_edge(1, 2)
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self.check_graph(G, is_planar=True)
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def test_goldner_harary(self):
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# test goldner-harary graph (a maximal planar graph)
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e = [
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(1, 2), (1, 3), (1, 4), (1, 5), (1, 7), (1, 8), (1, 10),
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(1, 11), (2, 3), (2, 4), (2, 6), (2, 7), (2, 9), (2, 10),
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(2, 11), (3, 4), (4, 5), (4, 6), (4, 7), (5, 7), (6, 7),
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(7, 8), (7, 9), (7, 10), (8, 10), (9, 10), (10, 11)
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]
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G = nx.Graph(e)
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self.check_graph(G, is_planar=True)
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def test_planar_multigraph(self):
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G = nx.MultiGraph([(1, 2), (1, 2), (1, 2), (1, 2), (2, 3), (3, 1)])
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self.check_graph(G, is_planar=True)
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def test_non_planar_multigraph(self):
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G = nx.MultiGraph(nx.complete_graph(5))
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G.add_edges_from([(1, 2)]*5)
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self.check_graph(G, is_planar=False)
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def test_planar_digraph(self):
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G = nx.DiGraph([
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(1, 2), (2, 3), (2, 4), (4, 1), (4, 2), (1, 4), (3, 2)
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])
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self.check_graph(G, is_planar=True)
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def test_non_planar_digraph(self):
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G = nx.DiGraph(nx.complete_graph(5))
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G.remove_edge(1, 2)
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G.remove_edge(4, 1)
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self.check_graph(G, is_planar=False)
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def test_single_component(self):
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# Test a graph with only a single node
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G = nx.Graph()
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G.add_node(1)
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self.check_graph(G, is_planar=True)
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def test_graph1(self):
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G = nx.OrderedGraph([
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(3, 10), (2, 13), (1, 13), (7, 11), (0, 8), (8, 13), (0, 2),
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(0, 7), (0, 10), (1, 7)
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])
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self.check_graph(G, is_planar=True)
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def test_graph2(self):
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G = nx.OrderedGraph([
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(1, 2), (4, 13), (0, 13), (4, 5), (7, 10), (1, 7), (0, 3), (2, 6),
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(5, 6), (7, 13), (4, 8), (0, 8), (0, 9), (2, 13), (6, 7), (3, 6),
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(2, 8)
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])
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self.check_graph(G, is_planar=False)
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def test_graph3(self):
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G = nx.OrderedGraph([
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(0, 7), (3, 11), (3, 4), (8, 9), (4, 11), (1, 7), (1, 13), (1, 11),
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(3, 5), (5, 7), (1, 3), (0, 4), (5, 11), (5, 13)
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])
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self.check_graph(G, is_planar=False)
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def test_counterexample_planar(self):
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with pytest.raises(nx.NetworkXException):
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# Try to get a counterexample of a planar graph
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G = nx.Graph()
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G.add_node(1)
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get_counterexample(G)
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def test_counterexample_planar_recursive(self):
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with pytest.raises(nx.NetworkXException):
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# Try to get a counterexample of a planar graph
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G = nx.Graph()
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G.add_node(1)
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get_counterexample_recursive(G)
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def check_embedding(G, embedding):
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"""Raises an exception if the combinatorial embedding is not correct
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Parameters
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----------
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G : NetworkX graph
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embedding : a dict mapping nodes to a list of edges
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This specifies the ordering of the outgoing edges from a node for
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a combinatorial embedding
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Notes
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-----
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Checks the following things:
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- The type of the embedding is correct
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- The nodes and edges match the original graph
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- Every half edge has its matching opposite half edge
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- No intersections of edges (checked by Euler's formula)
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"""
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if not isinstance(embedding, nx.PlanarEmbedding):
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raise nx.NetworkXException(
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"Bad embedding. Not of type nx.PlanarEmbedding")
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# Check structure
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embedding.check_structure()
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# Check that graphs are equivalent
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assert set(G.nodes) == set(embedding.nodes), "Bad embedding. Nodes don't match the original graph."
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# Check that the edges are equal
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g_edges = set()
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for edge in G.edges:
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if edge[0] != edge[1]:
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g_edges.add((edge[0], edge[1]))
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g_edges.add((edge[1], edge[0]))
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assert g_edges == set(embedding.edges), "Bad embedding. Edges don't match the original graph."
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def check_counterexample(G, sub_graph):
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"""Raises an exception if the counterexample is wrong.
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Parameters
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----------
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G : NetworkX graph
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subdivision_nodes : set
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A set of nodes inducing a subgraph as a counterexample
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"""
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# 1. Create the sub graph
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sub_graph = nx.Graph(sub_graph)
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# 2. Remove self loops
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for u in sub_graph:
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if sub_graph.has_edge(u, u):
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sub_graph.remove_edge(u, u)
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# keep track of nodes we might need to contract
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contract = list(sub_graph)
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# 3. Contract Edges
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while len(contract) > 0:
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contract_node = contract.pop()
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if contract_node not in sub_graph:
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# Node was already contracted
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continue
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degree = sub_graph.degree[contract_node]
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# Check if we can remove the node
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if degree == 2:
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# Get the two neighbors
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neighbors = iter(sub_graph[contract_node])
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u = next(neighbors)
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v = next(neighbors)
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# Save nodes for later
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contract.append(u)
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contract.append(v)
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# Contract edge
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sub_graph.remove_node(contract_node)
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sub_graph.add_edge(u, v)
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# 4. Check for isomorphism with K5 or K3_3 graphs
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if len(sub_graph) == 5:
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if not nx.is_isomorphic(nx.complete_graph(5), sub_graph):
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raise nx.NetworkXException("Bad counter example.")
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elif len(sub_graph) == 6:
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if not nx.is_isomorphic(nx.complete_bipartite_graph(3, 3), sub_graph):
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raise nx.NetworkXException("Bad counter example.")
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else:
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raise nx.NetworkXException("Bad counter example.")
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class TestPlanarEmbeddingClass:
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def test_get_data(self):
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embedding = self.get_star_embedding(3)
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data = embedding.get_data()
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data_cmp = {0: [2, 1], 1: [0], 2: [0]}
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assert data == data_cmp
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def test_missing_edge_orientation(self):
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with pytest.raises(nx.NetworkXException):
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embedding = nx.PlanarEmbedding()
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embedding.add_edge(1, 2)
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embedding.add_edge(2, 1)
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# Invalid structure because the orientation of the edge was not set
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embedding.check_structure()
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def test_invalid_edge_orientation(self):
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with pytest.raises(nx.NetworkXException):
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embedding = nx.PlanarEmbedding()
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embedding.add_half_edge_first(1, 2)
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embedding.add_half_edge_first(2, 1)
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embedding.add_edge(1, 3)
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embedding.check_structure()
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def test_missing_half_edge(self):
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with pytest.raises(nx.NetworkXException):
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embedding = nx.PlanarEmbedding()
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embedding.add_half_edge_first(1, 2)
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# Invalid structure because other half edge is missing
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embedding.check_structure()
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def test_not_fulfilling_euler_formula(self):
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with pytest.raises(nx.NetworkXException):
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embedding = nx.PlanarEmbedding()
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for i in range(5):
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for j in range(5):
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if i != j:
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embedding.add_half_edge_first(i, j)
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embedding.check_structure()
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def test_missing_reference(self):
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with pytest.raises(nx.NetworkXException):
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embedding = nx.PlanarEmbedding()
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embedding.add_half_edge_cw(1, 2, 3)
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def test_connect_components(self):
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embedding = nx.PlanarEmbedding()
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embedding.connect_components(1, 2)
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def test_successful_face_traversal(self):
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embedding = nx.PlanarEmbedding()
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embedding.add_half_edge_first(1, 2)
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embedding.add_half_edge_first(2, 1)
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face = embedding.traverse_face(1, 2)
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assert face == [1, 2]
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def test_unsuccessful_face_traversal(self):
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with pytest.raises(nx.NetworkXException):
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embedding = nx.PlanarEmbedding()
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embedding.add_edge(1, 2, ccw=2, cw=3)
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embedding.add_edge(2, 1, ccw=1, cw=3)
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embedding.traverse_face(1, 2)
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@staticmethod
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def get_star_embedding(n):
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embedding = nx.PlanarEmbedding()
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for i in range(1, n):
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embedding.add_half_edge_first(0, i)
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embedding.add_half_edge_first(i, 0)
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return embedding
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