def IcosahedralGraph():
"""
Returns an Icosahedral graph (with 12 nodes).
The regular icosahedron is a 20-sided triangular polyhedron. The
icosahedral graph corresponds to the connectivity of the vertices
of the icosahedron. It is dual to the dodecahedral graph. The
icosahedron is symmetric, so the spring-layout algorithm will be
very effective for display.
PLOTTING: The Icosahedral graph should be viewed in 3 dimensions.
We chose to use the default spring-layout algorithm here, so that
multiple iterations might yield a different point of reference for
the user. We hope to add rotatable, 3-dimensional viewing in the
future. In such a case, a string argument will be added to select
the flat spring-layout over a future implementation.
EXAMPLES: Construct and show an Octahedral graph
::
sage: g = graphs.IcosahedralGraph()
sage: g.show() # long time
Create several icosahedral graphs in a Sage graphics array. They
will be drawn differently due to the use of the spring-layout
algorithm.
::
sage: g = []
sage: j = []
sage: for i in range(9):
... k = graphs.IcosahedralGraph()
... g.append(k)
...
sage: for i in range(3):
... n = []
... for m in range(3):
... n.append(g[3*i + m].plot(vertex_size=50, vertex_labels=False))
... j.append(n)
...
sage: G = sage.plot.graphics.GraphicsArray(j)
sage: G.show() # long time
"""
import networkx
G = networkx.icosahedral_graph()
pos = {}
r1 = 5
r2 = 2
for i,v in enumerate([2,8,7,11,4,6]):
i = i + .5
pos[v] = (r1*cos(i*pi/3),r1*sin(i*pi/3))
for i,v in enumerate([1,9,0,10,5,3]):
i = i + .5
pos[v] = (r2*cos(i*pi/3),r2*sin(i*pi/3))
return graph.Graph(G, name="Icosahedron", pos = pos)
def test_icosahedral():
G=nx.icosahedral_graph()
for flow_func in flow_funcs:
assert_equal(5, nx.node_connectivity(G, flow_func=flow_func),
msg=msg.format(flow_func.__name__))
assert_equal(5, nx.edge_connectivity(G, flow_func=flow_func),
msg=msg.format(flow_func.__name__))
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 test_icosahedral():
G=nx.icosahedral_graph()
for flow_func in flow_funcs:
assert_equal(5, nx.node_connectivity(G, flow_func=flow_func),
msg=msg.format(flow_func.__name__))
assert_equal(5, nx.edge_connectivity(G, flow_func=flow_func),
msg=msg.format(flow_func.__name__))
def IcosahedralGraph():
"""
Returns an Icosahedral graph (with 12 nodes).
The regular icosahedron is a 20-sided triangular polyhedron. The
icosahedral graph corresponds to the connectivity of the vertices
of the icosahedron. It is dual to the dodecahedral graph. The
icosahedron is symmetric, so the spring-layout algorithm will be
very effective for display.
PLOTTING: The Icosahedral graph should be viewed in 3 dimensions.
We chose to use the default spring-layout algorithm here, so that
multiple iterations might yield a different point of reference for
the user. We hope to add rotatable, 3-dimensional viewing in the
future. In such a case, a string argument will be added to select
the flat spring-layout over a future implementation.
EXAMPLES: Construct and show an Octahedral graph
::
sage: g = graphs.IcosahedralGraph()
sage: g.show() # long time
Create several icosahedral graphs in a Sage graphics array. They
will be drawn differently due to the use of the spring-layout
algorithm.
::
sage: g = []
sage: j = []
sage: for i in range(9):
... k = graphs.IcosahedralGraph()
... g.append(k)
...
sage: for i in range(3):
... n = []
... for m in range(3):
... n.append(g[3*i + m].plot(vertex_size=50, vertex_labels=False))
... j.append(n)
...
sage: G = sage.plot.graphics.GraphicsArray(j)
sage: G.show() # long time
"""
import networkx
G = networkx.icosahedral_graph()
pos = {}
r1 = 5
r2 = 2
for i, v in enumerate([2, 8, 7, 11, 4, 6]):
i = i + .5
pos[v] = (r1 * cos(i * pi / 3), r1 * sin(i * pi / 3))
for i, v in enumerate([1, 9, 0, 10, 5, 3]):
i = i + .5
pos[v] = (r2 * cos(i * pi / 3), r2 * sin(i * pi / 3))
return graph.Graph(G, name="Icosahedron", pos=pos)
def test_intersection_array(self):
b, c = nx.intersection_array(nx.cycle_graph(5))
assert_equal(b, [2, 1])
assert_equal(c, [1, 1])
b, c = nx.intersection_array(nx.dodecahedral_graph())
assert_equal(b, [3, 2, 1, 1, 1])
assert_equal(c, [1, 1, 1, 2, 3])
b, c = nx.intersection_array(nx.icosahedral_graph())
assert_equal(b, [5, 2, 1])
assert_equal(c, [1, 2, 5])
def test_intersection_array(self):
b, c = nx.intersection_array(nx.cycle_graph(5))
assert b == [2, 1]
assert c == [1, 1]
b, c = nx.intersection_array(nx.dodecahedral_graph())
assert b == [3, 2, 1, 1, 1]
assert c == [1, 1, 1, 2, 3]
b, c = nx.intersection_array(nx.icosahedral_graph())
assert b == [5, 2, 1]
assert c == [1, 2, 5]
def test_intersection_array(self):
b,c=nx.intersection_array(nx.cycle_graph(5))
assert_equal(b,[2, 1])
assert_equal(c,[1, 1])
b,c=nx.intersection_array(nx.dodecahedral_graph())
assert_equal(b,[3, 2, 1, 1, 1])
assert_equal(c,[1, 1, 1, 2, 3])
b,c=nx.intersection_array(nx.icosahedral_graph())
assert_equal(b,[5, 2, 1])
assert_equal(c,[1, 2, 5])
def test_icosahedral_disjoint_paths():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge disjoint paths
edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
assert_true(are_edge_disjoint_paths(G, edge_dpaths), msg=msg.format(flow_func.__name__))
assert_equal(5, len(edge_dpaths), msg=msg.format(flow_func.__name__))
# node disjoint paths
node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
assert_true(are_node_disjoint_paths(G, node_dpaths), msg=msg.format(flow_func.__name__))
assert_equal(5, len(node_dpaths), msg=msg.format(flow_func.__name__))
def test_is_distance_regular(self):
assert_true(nx.is_distance_regular(nx.icosahedral_graph()))
assert_true(nx.is_distance_regular(nx.petersen_graph()))
assert_true(nx.is_distance_regular(nx.cubical_graph()))
assert_true(nx.is_distance_regular(nx.complete_bipartite_graph(3, 3)))
assert_true(nx.is_distance_regular(nx.tetrahedral_graph()))
assert_true(nx.is_distance_regular(nx.dodecahedral_graph()))
assert_true(nx.is_distance_regular(nx.pappus_graph()))
assert_true(nx.is_distance_regular(nx.heawood_graph()))
assert_true(nx.is_distance_regular(nx.cycle_graph(3)))
# no distance regular
assert_false(nx.is_distance_regular(nx.path_graph(4)))
def test_is_distance_regular(self):
assert_true(nx.is_distance_regular(nx.icosahedral_graph()))
assert_true(nx.is_distance_regular(nx.petersen_graph()))
assert_true(nx.is_distance_regular(nx.cubical_graph()))
assert_true(nx.is_distance_regular(nx.complete_bipartite_graph(3,3)))
assert_true(nx.is_distance_regular(nx.tetrahedral_graph()))
assert_true(nx.is_distance_regular(nx.dodecahedral_graph()))
assert_true(nx.is_distance_regular(nx.pappus_graph()))
assert_true(nx.is_distance_regular(nx.heawood_graph()))
assert_true(nx.is_distance_regular(nx.cycle_graph(3)))
# no distance regular
assert_false(nx.is_distance_regular(nx.path_graph(4)))
def gen():
# predefined graphs in networkx
# return nx.bull_graph() # 1-connected planar
# return nx.chvatal_graph() # 4-connected non-planar
# return nx.cubical_graph() # 3-connected planar
# return nx.desargues_graph() # 3-connected non-planar
# return nx.diamond_graph() # 2-connected planar
# return nx.dodecahedral_graph() # 3-connected planar
# return nx.frucht_graph() # 3-connected planar
# return nx.heawood_graph() # 3-connected planar
# return nx.house_graph() # 2-connected planar
# return nx.house_x_graph() # 2-connected planar
return nx.icosahedral_graph() # 5-connected planar
def test_icosahedral_disjoint_paths():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge disjoint paths
edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
assert 5 == len(edge_dpaths), errmsg
# node disjoint paths
node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
assert are_node_disjoint_paths(G, node_dpaths), errmsg
assert 5 == len(node_dpaths), errmsg
def test_icosahedral_disjoint_paths():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge disjoint paths
edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
assert_true(are_edge_disjoint_paths(G, edge_dpaths),
msg=msg.format(flow_func.__name__))
assert_equal(5, len(edge_dpaths), msg=msg.format(flow_func.__name__))
# node disjoint paths
node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
assert_true(are_node_disjoint_paths(G, node_dpaths),
msg=msg.format(flow_func.__name__))
assert_equal(5, len(node_dpaths), msg=msg.format(flow_func.__name__))
def test_icosahedral_cutset():
G = nx.icosahedral_graph()
# edge cuts
edge_cut = nx.minimum_edge_cut(G)
assert_equal(5, len(edge_cut))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H))
# node cuts
node_cut = nx.minimum_node_cut(G)
assert_equal(5, len(node_cut))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H))
def test_icosahedral_cutset():
G=nx.icosahedral_graph()
# edge cuts
edge_cut = nx.minimum_edge_cut(G)
assert_equal(5, len(edge_cut))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H))
# node cuts
node_cut = nx.minimum_node_cut(G)
assert_equal(5,len(node_cut))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H))
def test_icosahedral_cutset():
G=nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert_equal(5, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(5, len(node_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_icosahedral_cutset():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert_equal(5, len(edge_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_edges_from(edge_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert_equal(5, len(node_cut), msg=msg.format(flow_func.__name__))
H = G.copy()
H.remove_nodes_from(node_cut)
assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
def test_cutoff_disjoint_paths():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
for cutoff in [2, 4]:
kwargs['cutoff'] = cutoff
# edge disjoint paths
edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
assert are_edge_disjoint_paths(G, edge_dpaths), msg.format(
flow_func.__name__)
assert cutoff == len(edge_dpaths), msg.format(flow_func.__name__)
# node disjoint paths
node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
assert are_node_disjoint_paths(G, node_dpaths), msg.format(
flow_func.__name__)
assert cutoff == len(node_dpaths), msg.format(flow_func.__name__)
def test_icosahedral_cutset():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = dict(flow_func=flow_func)
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert 5 == len(edge_cut), errmsg
H = G.copy()
H.remove_edges_from(edge_cut)
assert not nx.is_connected(H), errmsg
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert 5 == len(node_cut), errmsg
H = G.copy()
H.remove_nodes_from(node_cut)
assert not nx.is_connected(H), errmsg
def platonic(n): # n must be 4, 6, 8, 12 or 20
# returns the matrix for sp2 platonic solid, with alpha = 0 and beta = -1
n_int = int(n)
if n_int == 4:
s = nx.tetrahedral_graph()
elif n_int == 6:
s = nx.cubical_graph()
elif n_int == 8:
s = nx.octahedral_graph()
elif n_int == 12:
s = nx.dodecahedral_graph()
elif n_int == 20:
s = nx.icosahedral_graph()
else:
print("n must be equal to 4, 6, 8, 12 or 20")
M = -nx.adjacency_matrix(s)
return M.todense()
def test_all_pairs_connectivity_icosahedral(self):
G = nx.icosahedral_graph()
C = nx.all_pairs_node_connectivity(G)
assert_true(all(5 == C[u][v] for u, v in itertools.combinations(G, 2)))
seed = 123
# most used graphs
G1 = nx.erdos_renyi_graph(n=24, p=0.3, seed=seed)
# some cool graphs
G2 = nx.star_graph(20)
G3 = nx.path_graph(30)
G4 = nx.petersen_graph()
G5 = nx.dodecahedral_graph()
G6 = nx.house_graph()
G7 = nx.moebius_kantor_graph()
G8 = nx.barabasi_albert_graph(5, 4)
G9 = nx.heawood_graph()
G10 = nx.icosahedral_graph()
G11 = nx.sedgewick_maze_graph()
G12 = nx.havel_hakimi_graph([1, 1])
G13 = nx.complete_graph(20)
G14 = nx.bull_graph()
G = G1 # choose a graph from the list
gd.draw_custom(G)
plt.show()
#exact cut
print("Time 'local_consistent_max_cut':" + str(gt.execution_time(mc.local_consistent_max_cut, 1, G)))
print('Edges cut: ' + str(gc.cut_edges(G)))
print('\n')
print("Time 'lazy_local_consistent_max_cut':" + str(gt.execution_time(mc.lazy_local_consistent_max_cut, 1, G)))
def test_icosahedral():
G = nx.icosahedral_graph()
assert_equal(5, nx.node_connectivity(G))
assert_equal(5, nx.edge_connectivity(G))
def test_properties_named_small_graphs(self):
G = nx.bull_graph()
assert G.number_of_nodes() == 5
assert G.number_of_edges() == 5
assert sorted(d for n, d in G.degree()) == [1, 1, 2, 3, 3]
assert nx.diameter(G) == 3
assert nx.radius(G) == 2
G = nx.chvatal_graph()
assert G.number_of_nodes() == 12
assert G.number_of_edges() == 24
assert list(d for n, d in G.degree()) == 12 * [4]
assert nx.diameter(G) == 2
assert nx.radius(G) == 2
G = nx.cubical_graph()
assert G.number_of_nodes() == 8
assert G.number_of_edges() == 12
assert list(d for n, d in G.degree()) == 8 * [3]
assert nx.diameter(G) == 3
assert nx.radius(G) == 3
G = nx.desargues_graph()
assert G.number_of_nodes() == 20
assert G.number_of_edges() == 30
assert list(d for n, d in G.degree()) == 20 * [3]
G = nx.diamond_graph()
assert G.number_of_nodes() == 4
assert sorted(d for n, d in G.degree()) == [2, 2, 3, 3]
assert nx.diameter(G) == 2
assert nx.radius(G) == 1
G = nx.dodecahedral_graph()
assert G.number_of_nodes() == 20
assert G.number_of_edges() == 30
assert list(d for n, d in G.degree()) == 20 * [3]
assert nx.diameter(G) == 5
assert nx.radius(G) == 5
G = nx.frucht_graph()
assert G.number_of_nodes() == 12
assert G.number_of_edges() == 18
assert list(d for n, d in G.degree()) == 12 * [3]
assert nx.diameter(G) == 4
assert nx.radius(G) == 3
G = nx.heawood_graph()
assert G.number_of_nodes() == 14
assert G.number_of_edges() == 21
assert list(d for n, d in G.degree()) == 14 * [3]
assert nx.diameter(G) == 3
assert nx.radius(G) == 3
G = nx.hoffman_singleton_graph()
assert G.number_of_nodes() == 50
assert G.number_of_edges() == 175
assert list(d for n, d in G.degree()) == 50 * [7]
assert nx.diameter(G) == 2
assert nx.radius(G) == 2
G = nx.house_graph()
assert G.number_of_nodes() == 5
assert G.number_of_edges() == 6
assert sorted(d for n, d in G.degree()) == [2, 2, 2, 3, 3]
assert nx.diameter(G) == 2
assert nx.radius(G) == 2
G = nx.house_x_graph()
assert G.number_of_nodes() == 5
assert G.number_of_edges() == 8
assert sorted(d for n, d in G.degree()) == [2, 3, 3, 4, 4]
assert nx.diameter(G) == 2
assert nx.radius(G) == 1
G = nx.icosahedral_graph()
assert G.number_of_nodes() == 12
assert G.number_of_edges() == 30
assert (list(
d for n, d in G.degree()) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])
assert nx.diameter(G) == 3
assert nx.radius(G) == 3
G = nx.krackhardt_kite_graph()
assert G.number_of_nodes() == 10
assert G.number_of_edges() == 18
assert (sorted(
d for n, d in G.degree()) == [1, 2, 3, 3, 3, 4, 4, 5, 5, 6])
G = nx.moebius_kantor_graph()
assert G.number_of_nodes() == 16
assert G.number_of_edges() == 24
assert list(d for n, d in G.degree()) == 16 * [3]
assert nx.diameter(G) == 4
G = nx.octahedral_graph()
assert G.number_of_nodes() == 6
assert G.number_of_edges() == 12
assert list(d for n, d in G.degree()) == 6 * [4]
assert nx.diameter(G) == 2
assert nx.radius(G) == 2
G = nx.pappus_graph()
assert G.number_of_nodes() == 18
assert G.number_of_edges() == 27
assert list(d for n, d in G.degree()) == 18 * [3]
assert nx.diameter(G) == 4
G = nx.petersen_graph()
assert G.number_of_nodes() == 10
assert G.number_of_edges() == 15
assert list(d for n, d in G.degree()) == 10 * [3]
assert nx.diameter(G) == 2
assert nx.radius(G) == 2
G = nx.sedgewick_maze_graph()
assert G.number_of_nodes() == 8
assert G.number_of_edges() == 10
assert sorted(d for n, d in G.degree()) == [1, 2, 2, 2, 3, 3, 3, 4]
G = nx.tetrahedral_graph()
assert G.number_of_nodes() == 4
assert G.number_of_edges() == 6
assert list(d for n, d in G.degree()) == [3, 3, 3, 3]
assert nx.diameter(G) == 1
assert nx.radius(G) == 1
G = nx.truncated_cube_graph()
assert G.number_of_nodes() == 24
assert G.number_of_edges() == 36
assert list(d for n, d in G.degree()) == 24 * [3]
G = nx.truncated_tetrahedron_graph()
assert G.number_of_nodes() == 12
assert G.number_of_edges() == 18
assert list(d for n, d in G.degree()) == 12 * [3]
G = nx.tutte_graph()
assert G.number_of_nodes() == 46
assert G.number_of_edges() == 69
assert list(d for n, d in G.degree()) == 46 * [3]
# Test create_using with directed or multigraphs on small graphs
pytest.raises(nx.NetworkXError,
nx.tutte_graph,
create_using=nx.DiGraph)
MG = nx.tutte_graph(create_using=nx.MultiGraph)
assert sorted(MG.edges()) == sorted(G.edges())
def small_graphs():
print("Make small graph")
G = nx.make_small_graph(
["adjacencylist", "C_4", 4, [[2, 4], [1, 3], [2, 4], [1, 3]]])
draw_graph(G)
G = nx.make_small_graph(
["adjacencylist", "C_4", 4, [[2, 4], [3], [4], []]])
draw_graph(G)
G = nx.make_small_graph(
["edgelist", "C_4", 4, [[1, 2], [3, 4], [2, 3], [4, 1]]])
draw_graph(G)
print("LCF graph")
G = nx.LCF_graph(6, [3, -3], 3)
draw_graph(G)
G = nx.LCF_graph(14, [5, -5], 7)
draw_graph(G)
print("Bull graph")
G = nx.bull_graph()
draw_graph(G)
print("Chvátal graph")
G = nx.chvatal_graph()
draw_graph(G)
print("Cubical graph")
G = nx.cubical_graph()
draw_graph(G)
print("Desargues graph")
G = nx.desargues_graph()
draw_graph(G)
print("Diamond graph")
G = nx.diamond_graph()
draw_graph(G)
print("Dodechaedral graph")
G = nx.dodecahedral_graph()
draw_graph(G)
print("Frucht graph")
G = nx.frucht_graph()
draw_graph(G)
print("Heawood graph")
G = nx.heawood_graph()
draw_graph(G)
print("House graph")
G = nx.house_graph()
draw_graph(G)
print("House X graph")
G = nx.house_x_graph()
draw_graph(G)
print("Icosahedral graph")
G = nx.icosahedral_graph()
draw_graph(G)
print("Krackhardt kite graph")
G = nx.krackhardt_kite_graph()
draw_graph(G)
print("Moebius kantor graph")
G = nx.moebius_kantor_graph()
draw_graph(G)
print("Octahedral graph")
G = nx.octahedral_graph()
draw_graph(G)
print("Pappus graph")
G = nx.pappus_graph()
draw_graph(G)
print("Petersen graph")
G = nx.petersen_graph()
draw_graph(G)
print("Sedgewick maze graph")
G = nx.sedgewick_maze_graph()
draw_graph(G)
print("Tetrahedral graph")
G = nx.tetrahedral_graph()
draw_graph(G)
print("Truncated cube graph")
G = nx.truncated_cube_graph()
draw_graph(G)
print("Truncated tetrahedron graph")
G = nx.truncated_tetrahedron_graph()
draw_graph(G)
print("Tutte graph")
G = nx.tutte_graph()
draw_graph(G)
import networkx as nx
import matplotlib.pylab as plt
from plot_multigraph import plot_multigraph
graphs = [
("bull", nx.bull_graph()),
("chvatal", nx.chvatal_graph()),
("cubical", nx.cubical_graph()),
("desargues", nx.desargues_graph()),
("diamond", nx.diamond_graph()),
("dodecahedral", nx.dodecahedral_graph()),
("frucht", nx.frucht_graph()),
("heawood", nx.heawood_graph()),
("house", nx.house_graph()),
("house_x", nx.house_x_graph()),
("icosahedral", nx.icosahedral_graph()),
("krackhardt_kite", nx.krackhardt_kite_graph()),
("moebius_kantor", nx.moebius_kantor_graph()),
("octahedral", nx.octahedral_graph()),
("pappus", nx.pappus_graph()),
("petersen", nx.petersen_graph()),
("sedgewick_maze", nx.sedgewick_maze_graph()),
("tetrahedral", nx.tetrahedral_graph()),
("truncated_cube", nx.truncated_cube_graph()),
("truncated_tetrahedron", nx.truncated_tetrahedron_graph()),
]
plot_multigraph(graphs, 4, 5, node_size=50)
plt.savefig('graphs/small.png')
del g[u][v]['visited']
if __name__ == '__main__':
targets = {
'bull': nx.bull_graph(), # 1-connected planar
'chvatal': nx.chvatal_graph(), # 4-connected non-planar
'cubical': nx.cubical_graph(), # 3-connected planar
'desargues': nx.desargues_graph(), # 3-connected non-planar
'diamond': nx.diamond_graph(), # 2-connected planar
'dodecahedral': nx.dodecahedral_graph(), # 3-connected planar
'frucht': nx.frucht_graph(), # 3-connected planar
'heawood': nx.heawood_graph(), # 3-connected non-planar
'house': nx.house_graph(), # 2-connected planar
'house_x': nx.house_x_graph(), # 2-connected planar
'icosahedral': nx.icosahedral_graph(), # 5-connected planar
'krackhardt': nx.krackhardt_kite_graph(), # 1-connected planar
'moebius': nx.moebius_kantor_graph(), # non-planar
'octahedral': nx.octahedral_graph(), # 4-connected planar
'pappus': nx.pappus_graph(), # 3-connected non-planar
'petersen': nx.petersen_graph(), # 3-connected non-planar
'sedgewick': nx.sedgewick_maze_graph(), # 1-connected planar
'tetrahedral': nx.tetrahedral_graph(), # 3-connected planar
'truncated_cube': nx.truncated_cube_graph(), # 3-conn. planar
'truncated_tetrahedron': nx.truncated_tetrahedron_graph(),
# 3-connected planar
'tutte': nx.tutte_graph()
} # 3-connected planar
for g_name, g in targets.items():
print g_name, is_planar(g)
def test_icosahedral():
G=nx.icosahedral_graph()
assert_equal(5, approx.node_connectivity(G))
assert_equal(5, approx.node_connectivity(G, 0, 5))
import networkx as nx
import matplotlib.pylab as plt
from plot_multigraph import plot_multigraph
graphs = [
("bull", nx.bull_graph()),
("chvatal", nx.chvatal_graph()),
("cubical", nx.cubical_graph()),
("desargues", nx.desargues_graph()),
("diamond", nx.diamond_graph()),
("dodecahedral", nx.dodecahedral_graph()),
("frucht", nx.frucht_graph()),
("heawood", nx.heawood_graph()),
("house", nx.house_graph()),
("house_x", nx.house_x_graph()),
("icosahedral", nx.icosahedral_graph()),
("krackhardt_kite", nx.krackhardt_kite_graph()),
("moebius_kantor", nx.moebius_kantor_graph()),
("octahedral", nx.octahedral_graph()),
("pappus", nx.pappus_graph()),
("petersen", nx.petersen_graph()),
("sedgewick_maze", nx.sedgewick_maze_graph()),
("tetrahedral", nx.tetrahedral_graph()),
("truncated_cube", nx.truncated_cube_graph()),
("truncated_tetrahedron", nx.truncated_tetrahedron_graph()),
]
plot_multigraph(graphs, 4, 5, node_size=50)
plt.savefig('graphs/small.png')
def test_icosahedral():
G=nx.icosahedral_graph()
assert_equal(5, nx.node_connectivity(G))
assert_equal(5, nx.edge_connectivity(G))
def test_all_pairs_connectivity_icosahedral(self):
G = nx.icosahedral_graph()
C = nx.all_pairs_node_connectivity(G)
assert_true(all(5 == C[u][v] for u, v in itertools.combinations(G, 2)))
return list(approx.max_clique(graph))
# print selected_comm.number_of_nodes()
# max_size_clique = nx.graph_clique_number(selected_comm)
# print max_size_clique
# for cl in nx.find_cliques(selected_comm):
# if len(cl) == max_size_clique:
# return cl
# #print len(cl), cl
#print nx.find_cliques(selected_comm)
def choose_nodes_from_graph(graph, num_players, num_seeds, setup2):
leftover = num_seeds - len(setup2)
if leftover > 0:
lst = setup2 + r.sample(graph.nodes(), leftover)
else:
lst = r.sample(setup2, num_seeds)
return lst
if __name__ == '__main__':
g = nx.icosahedral_graph()
setup = setup(g, 2, 2)
print setup
print choose_nodes_from_graph(g, 2, 2, setup)
viewer.draw_graph(g)
try:
plt.show()
except:
plt.hide()
def test_icosahedral():
G = nx.icosahedral_graph()
assert_equal(5, approx.node_connectivity(G))
assert_equal(5, approx.node_connectivity(G, 0, 5))
def test_icosahedral():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
errmsg = f"Assertion failed in function: {flow_func.__name__}"
assert 5 == nx.node_connectivity(G, flow_func=flow_func), errmsg
assert 5 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
def test_icosahedral(self):
expected = True
actual = is_planar(nx.icosahedral_graph())
self.assertEqual(expected, actual)
