def test180_tutte_cage_graph(self):
""" Tutte 12-cage graph. """
g = nx.LCF_graph(126, [17, 27, -13, -59, -35, 35, -11, 13, -53\
, 53, -27, 21, 57, 11, -21, -57, 59, -17], 7)
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test142_utility_graph(self):
""" Larger utility graph from LCF notation. """
g = nx.LCF_graph(60, [3, -3], 3)
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test142_utility_graph")
self.assertEqual( len(mate1), len(mate2) )
def test025_barbell_graph(self):
""" Very small barbell graph. """
g = nx.barbell_graph(9, 2)
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate2, "test025_barbell_graph_edmonds")
mate1 = mv.max_cardinality_matching( g )
self.assertEqual( len(mate1), len(mate2) )
def test103_lollipop_graph(self):
""" Large lollipop graph. """
g = nx.lollipop_graph(17, 11)
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test103_lollipop_graph")
self.assertEqual( len(mate1), len(mate2) )
def test200_icosahedralgraph(self):
""" Icosahedral graph. """
g = nx.icosahedral_graph()
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
#td.showGraph(g, mate1, "test200_icosahedralgraph")
self.assertEqual( len(mate1), len(mate2) )
def test090_singlebloom(self):
""" Single bloom, two edge extensions, case 1. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,1),(3,6)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test030_twoedges(self):
""" Two edges. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test083_barabasi_albert_graph(self):
""" Random graph using Barabasi-Albert preferential
attachment model. """
g = nx.barabasi_albert_graph(100, 5)
mate1 = mv.max_cardinality_matching(g)
mate2 = nx.max_weight_matching(g, True)
self.assertEqual(len(mate1), len(mate2))
def test040_threeedges(self):
""" Three edges, linear. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test170_bullgraph(self):
""" Bull graph. """
g = nx.bull_graph()
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
#td.showGraph(g, mate1, "test170_bullgraph")
self.assertEqual( len(mate1), len(mate2) )
def test190_octahedralgraph(self):
""" Octahedral graph. """
g = nx.octahedral_graph()
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test190_octahedralgraph")
self.assertEqual( len(mate1), len(mate2) )
def test050_linear(self):
""" Multiple edges, linear. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,6)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test160_petersengraph(self):
""" Petersen graph. """
g = nx.petersen_graph()
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test160_petersengraph")
self.assertEqual( len(mate1), len(mate2) )
def test070_circle(self):
""" Multiple edges, circle of even length. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,0)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test020_singleedge(self):
""" Single edge. """
g = nx.Graph()
g.add_edge(0,1)
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
self.assertEqual( len(mate1), len(mate2) )
def test035_dense_gnm_random_graph(self):
""" Larger random graph picked from set of all graphs
with n nodes and m edges. """
g = nx.dense_gnm_random_graph(300, 10000)
mate1 = mv.max_cardinality_matching(g)
mate2 = nx.max_weight_matching(g, True)
self.assertEqual(len(mate1), len(mate2))
def test142_doublebloom(self):
""" Two blooms, connected together by one edge. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,0),(3,6),(6,7),(7,8),(8,9),(9,10),(10,6)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test142_doublebloom")
self.assertEqual( len(mate1), len(mate2) )
def test220_fruchtgraph(self):
""" Frucht graph, smallest cubical graph. """
g = nx.frucht_graph()
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test220_fruchtgraph")
td.showGraph(g, mate2, "test220_fruchtgraph_edmonds")
self.assertEqual( len(mate1), len(mate2) )
def test149_doublebloom(self):
""" Two blooms, one embedded, connected at their centers. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(4,6),(4,1),(3,4),(4,0),(3,7),(7,8),(8,9),(9,10),(10,3)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test149_doublebloom")
self.assertEqual( len(mate1), len(mate2) )
def test145_doublebloom(self):
""" Two blooms, with three vertices, connected by one edge. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,0),(2,3),(3,4),(4,5),(5,3),(4,6),(6,7),(7,8),(8,6)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test145_doublebloom")
self.assertEqual( len(mate1), len(mate2) )
def test120_singlebloom(self):
""" Single bloom, three connected components. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,0),(3,1),(3,5)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test120_singlebloom")
self.assertEqual( len(mate1), len(mate2) )
def test080_singlebloom(self):
""" Single bloom, one edge extension. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,1)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test080_singlebloom")
self.assertEqual( len(mate1), len(mate2) )
def test151_triplebloom(self):
""" Three blooms, connected together with three bridges. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,0),(3,5),(5,6),(15,11),(11,12),(12,13)\
,(13,14),(14,15),(6,7),(7,8),(8,9),(9,10),(10,6),(5,15)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test151_triplebloom")
self.assertEqual( len(mate1), len(mate2) )
def test146_doublebloom(self):
""" Two blooms, one embedded inside the other, last example in paper. """
g = nx.Graph()
g.add_edges_from([(0,2),(2,1),(2,5),(1,4),(1,3),(3,4),(4,5),(3,6),(6,7),(7,8),(7,10)\
,(5,10),(8,9),(10,11),(9,11),(11,12),(12,13)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test146_doublebloom")
self.assertEqual( len(mate1), len(mate2) )
def test240_disconnected_blooms(self):
""" Two blooms, connected together by two edges with another disconnected bloom graph. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,0),(3,5),(5,6),(6,7),(7,8),(8,9),(9,10)\
,(10,6),(11,12),(12,13),(14,15),(15,11),(12,14),(13,14)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test240_disconnected_blooms")
self.assertEqual( len(mate1), len(mate2) )
def test260_inter_blooms(self):
""" Two blooms, connected together. """
g = nx.Graph()
g.add_edges_from([(1,2),(2,3),(3,4),(4,5),(5,1),(5,6),(6,7),(4,6)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test260_inter_blooms")
self.assertEqual( len(mate1), len(mate2) )
def test280_pentagon_graph(self):
""" Two blooms, connected together. """
g = nx.Graph()
g.add_edges_from([(1,2),(2,3),(1,3),(3,4),(3,5),(4,5),(5,6),(6,7),(5,7),(7,8),(8,9),(7,9),
(9,10),(10,2),(2,9)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test280_pentagon_graph")
self.assertEqual( len(mate1), len(mate2) )
def test271_grid_graph(self):
""" Two blooms, connected together. """
g = nx.Graph()
g.add_edges_from([(1,2),(2,3),(3,4),(5,6),(6,7),(7,8), (9,10),(10,11),(11,12),(13,14),(14,15),(15,16),
(1,5),(5,9),(9,13),(2,6),(6,10),(10,14),(3,7),(7,11),(11,15),(4,8),(8,12),(12,16),(16,17),(13,18)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test271_Grid_Graphs")
self.assertEqual( len(mate1), len(mate2) )
def test211_cubicgraph(self):
""" Cubic graph with three connected blooms that is slightly different. """
g = nx.Graph()
g.add_edges_from([(0,1),(0,2),(0,3),(1,2),(2,3),(1,4),(3,4),(4,5),(5,6),(5,7),(6,8)\
,(6,9),(8,10),(9,10),(10,11),(11,8),(11,9),(7,12),(7,14),(12,13)\
,(13,14),(15,13),(15,12),(15,14),(12,14),(1,3),(8,9)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test211_cubicgraph")
td.showGraph(g, mate2, "test211_cubicgraph_edmonds")
self.assertEqual( len(mate1), len(mate2) )
def test230_flowersnarkgraph(self):
""" Flower snark J5, a flower snark with 20 vertices and 30 edges. """
g = nx.Graph()
g.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9),(9,10)\
,(10,11),(11,12),(12,13),(13,14),(14,0),(15,16),(16,17),(17,18)\
,(18,19),(19,15),(0,15),(1,11),(2,7),(3,16),(4,14),(5,10),(6,17)\
,(8,13),(9,18),(12,19)])
mate1 = mv.max_cardinality_matching( g )
mate2 = nx.max_weight_matching( g, True )
td.showGraph(g, mate1, "test230_flowersnarkgraph")
td.showGraph(g, mate2, "test230_flowersnarkgraph_edmonds")
self.assertEqual( len(mate1), len(mate2) )