def setUp(self):
# G is the example graph in Figure 1 from Batagelj and
# Zaversnik's paper titled An O(m) Algorithm for Cores
# Decomposition of Networks, 2003,
# http://arXiv.org/abs/cs/0310049. With nodes labeled as
# shown, the 3-core is given by nodes 1-8, the 2-core by nodes
# 9-16, the 1-core by nodes 17-20 and node 21 is in the
# 0-core.
t1 = nx.convert_node_labels_to_integers(nx.tetrahedral_graph(), 1)
t2 = nx.convert_node_labels_to_integers(t1, 5)
G = nx.union(t1, t2)
G.add_edges_from([(3, 7), (2, 11), (11, 5), (11, 12), (5, 12),
(12, 19), (12, 18), (3, 9), (7, 9), (7, 10),
(9, 10), (9, 20), (17, 13), (13, 14), (14, 15),
(15, 16), (16, 13)])
G.add_node(21)
self.G = G
# Create the graph H resulting from the degree sequence
# [0, 1, 2, 2, 2, 2, 3] when using the Havel-Hakimi algorithm.
degseq = [0, 1, 2, 2, 2, 2, 3]
H = nx.havel_hakimi_graph(degseq)
mapping = {6: 0, 0: 1, 4: 3, 5: 6, 3: 4, 1: 2, 2: 5}
self.H = nx.relabel_nodes(H, mapping)
def setUp(self):
# G is the example graph in Figure 1 from Batagelj and
# Zaversnik's paper titled An O(m) Algorithm for Cores
# Decomposition of Networks, 2003,
# http://arXiv.org/abs/cs/0310049. With nodes labeled as
# shown, the 3-core is given by nodes 1-8, the 2-core by nodes
# 9-16, the 1-core by nodes 17-20 and node 21 is in the
# 0-core.
t1 = nx.convert_node_labels_to_integers(nx.tetrahedral_graph(), 1)
t2 = nx.convert_node_labels_to_integers(t1, 5)
G = nx.union(t1, t2)
G.add_edges_from([(3, 7), (2, 11), (11, 5), (11, 12), (5, 12),
(12, 19), (12, 18), (3, 9), (7, 9), (7, 10), (9, 10),
(9, 20), (17, 13), (13, 14), (14, 15), (15, 16),
(16, 13)])
G.add_node(21)
self.G = G
# Create the graph H resulting from the degree sequence
# [0, 1, 2, 2, 2, 2, 3] when using the Havel-Hakimi algorithm.
degseq = [0, 1, 2, 2, 2, 2, 3]
H = nx.havel_hakimi_graph(degseq)
mapping = {6: 0, 0: 1, 4: 3, 5: 6, 3: 4, 1: 2, 2: 5}
self.H = nx.relabel_nodes(H, mapping)
def TetrahedralGraph():
"""
Returns a tetrahedral graph (with 4 nodes).
A tetrahedron is a 4-sided triangular pyramid. The tetrahedral
graph corresponds to the connectivity of the vertices of the
tetrahedron. This graph is equivalent to a wheel graph with 4 nodes
and also a complete graph on four nodes. (See examples below).
PLOTTING: The tetrahedral 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 a Tetrahedral graph
::
sage: g = graphs.TetrahedralGraph()
sage: g.show() # long time
The following example requires networkx::
sage: import networkx as NX
Compare this Tetrahedral, Wheel(4), Complete(4), and the
Tetrahedral plotted with the spring-layout algorithm below in a
Sage graphics array::
sage: tetra_pos = graphs.TetrahedralGraph()
sage: tetra_spring = Graph(NX.tetrahedral_graph())
sage: wheel = graphs.WheelGraph(4)
sage: complete = graphs.CompleteGraph(4)
sage: g = [tetra_pos, tetra_spring, wheel, complete]
sage: j = []
sage: for i in range(2):
....: n = []
....: for m in range(2):
....: n.append(g[i + m].plot(vertex_size=50, vertex_labels=False))
....: j.append(n)
sage: G = graphics_array(j)
sage: G.show() # long time
"""
import networkx
G = networkx.tetrahedral_graph()
return Graph(G,
name="Tetrahedron",
pos={
0: (0, 0),
1: (0, 1),
2: (cos(3.5 * pi / 3), sin(3.5 * pi / 3)),
3: (cos(5.5 * pi / 3), sin(5.5 * pi / 3))
})
def classic_small_graphs():
petersen = nx.petersen_graph()
tutte = nx.tutte_graph()
maze = nx.sedgewick_maze_graph()
tet = nx.tetrahedral_graph()
g_list = [petersen, tutte, maze, tet]
for n, g in enumerate(g_list):
plt.subplot(221+n)
nx.draw(g, with_labels=True, font_weight='bold')
plt.show()
def practice():
Peterson = nx.petersen_graph()
tutte = nx.tutte_graph()
maze = nx.sedgewick_maze_graph()
tet = nx.tetrahedral_graph()
G = nx.random_tree(20)
nx.draw(G, pos=nx.spring_layout(G), with_labels=True)
#nx.draw_shell(G, nlist=[range(5, 10), range(5)], with_labels=True, font_weight='bold')
plt.show()
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 TetrahedralGraph():
"""
Returns a tetrahedral graph (with 4 nodes).
A tetrahedron is a 4-sided triangular pyramid. The tetrahedral
graph corresponds to the connectivity of the vertices of the
tetrahedron. This graph is equivalent to a wheel graph with 4 nodes
and also a complete graph on four nodes. (See examples below).
PLOTTING: The tetrahedral 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 a Tetrahedral graph
::
sage: g = graphs.TetrahedralGraph()
sage: g.show() # long time
The following example requires networkx::
sage: import networkx as NX
Compare this Tetrahedral, Wheel(4), Complete(4), and the
Tetrahedral plotted with the spring-layout algorithm below in a
Sage graphics array::
sage: tetra_pos = graphs.TetrahedralGraph()
sage: tetra_spring = Graph(NX.tetrahedral_graph())
sage: wheel = graphs.WheelGraph(4)
sage: complete = graphs.CompleteGraph(4)
sage: g = [tetra_pos, tetra_spring, wheel, complete]
sage: j = []
sage: for i in range(2):
... n = []
... for m in range(2):
... n.append(g[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.tetrahedral_graph()
return graph.Graph(G, name="Tetrahedron", pos =
{ 0 : (0, 0),
1 : (0, 1),
2 : (cos(3.5*pi/3), sin(3.5*pi/3)),
3 : (cos(5.5*pi/3), sin(5.5*pi/3))}
)
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_tensor_product_classic_result():
K2 = nx.complete_graph(2)
G = nx.petersen_graph()
G = tensor_product(G,K2)
assert_true(nx.is_isomorphic(G,nx.desargues_graph()))
G = nx.cycle_graph(5)
G = tensor_product(G,K2)
assert_true(nx.is_isomorphic(G,nx.cycle_graph(10)))
G = nx.tetrahedral_graph()
G = tensor_product(G,K2)
assert_true(nx.is_isomorphic(G,nx.cubical_graph()))
def test_tensor_product_classic_result():
K2 = nx.complete_graph(2)
G = nx.petersen_graph()
G = nx.tensor_product(G, K2)
assert_true(nx.is_isomorphic(G, nx.desargues_graph()))
G = nx.cycle_graph(5)
G = nx.tensor_product(G, K2)
assert_true(nx.is_isomorphic(G, nx.cycle_graph(10)))
G = nx.tetrahedral_graph()
G = nx.tensor_product(G, K2)
assert_true(nx.is_isomorphic(G, nx.cubical_graph()))
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_tensor_product():
null=nx.null_graph()
empty1=nx.empty_graph(1)
empty10=nx.empty_graph(10)
K2=nx.complete_graph(2)
K3=nx.complete_graph(3)
K5=nx.complete_graph(5)
K10=nx.complete_graph(10)
P2=nx.path_graph(2)
P3=nx.path_graph(3)
P5=nx.path_graph(5)
P10=nx.path_graph(10)
# null graph
G=tensor_product(null,null)
assert_true(nx.is_isomorphic(G,null))
# null_graph X anything = null_graph and v.v.
G=tensor_product(null,empty10)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(null,K3)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(null,K10)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(null,P3)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(null,P10)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(empty10,null)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(K3,null)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(K10,null)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(P3,null)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(P10,null)
assert_true(nx.is_isomorphic(G,null))
G=tensor_product(P5,K3)
assert_equal(nx.number_of_nodes(G),5*3)
G=tensor_product(K3,K5)
assert_equal(nx.number_of_nodes(G),3*5)
G = nx.petersen_graph()
G = tensor_product(G,K2)
assert_true(nx.is_isomorphic(G,nx.desargues_graph()))
G = nx.cycle_graph(5)
G = tensor_product(G,K2)
assert_true(nx.is_isomorphic(G,nx.cycle_graph(10)))
G = nx.tetrahedral_graph()
G = tensor_product(G,K2)
assert_true(nx.is_isomorphic(G,nx.cubical_graph()))
G = nx.erdos_renyi_graph(10,2/10.)
H = nx.erdos_renyi_graph(10,2/10.)
GH = tensor_product(G,H)
for (u_G,u_H) in GH.nodes_iter():
for (v_G,v_H) in GH.nodes_iter():
if H.has_edge(u_H,v_H) and G.has_edge(u_G,v_G):
assert_true(GH.has_edge((u_G,u_H),(v_G,v_H)))
else:
assert_true(not GH.has_edge((u_G,u_H),(v_G,v_H)))
def test_tetrahedral(self):
expected = True
actual = is_planar(nx.tetrahedral_graph())
self.assertEqual(expected, actual)
# 典型的なグラフ操作
# subgraph(G, nbunch) - induce subgraph of G on nodes in nbunch
# union(G1,G2) - graph union
# disjoint_union(G1,G2) - graph union assuming all nodes are different
# cartesian_product(G1,G2) - return Cartesian product graph
# compose(G1,G2) - combine graphs identifying nodes common to both
# complement(G) - graph complement
# create_empty_copy(G) - return an empty copy of the same graph class
# convert_to_undirected(G) - return an undirected representation of G
# convert_to_directed(G) - return a directed representation of G
petersen=nx.petersen_graph() # ピーターセングラフ 10個の頂点と15個の辺からなる無向グラフ。グラフ理論の様々な問題の例、あるいは反例としてよく使われる。
tutte=nx.tutte_graph() # Tutte グラフ
maze=nx.sedgewick_maze_graph()
tet=nx.tetrahedral_graph() # テトラへドラル
K_5=nx.complete_graph(5) # 完全グラフ
K_3_5=nx.complete_bipartite_graph(3,5) #完全二部グラフ 2部グラフのうち特に第1の集合に属するそれぞれの頂点から第2の集合に属する全ての頂点に辺が伸びているもの
barbell=nx.barbell_graph(10,10) #
lollipop=nx.lollipop_graph(10,20) #
er=nx.erdos_renyi_graph(100,0.15)
ws=nx.watts_strogatz_graph(30,3,0.1)
ba=nx.barabasi_albert_graph(100,5)
red=nx.random_lobster(100,0.9,0.9)
nx.write_gml(red,"path.to.file")
mygraph=nx.read_gml("path.to.file")
# グラフの分析
def test_tetrahedral():
# Actual coefficient is 1
G = nx.tetrahedral_graph()
assert_equal(average_clustering(G, trials=int(len(G) / 2)),
nx.average_clustering(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')
def random(cls, number):
#return nx.random_geometric_graph(number, 0.125)
#return nx.petersen_graph()
return nx.tetrahedral_graph()
'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)
# g = nx.petersen_graph()
# g = nx.frucht_graph()
# g = nx.krackhardt_kite_graph()
# g = nx.icosahedral_graph()
# g = nx.tutte_graph()
# print is_planarity(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 test_tetrahedral():
# Actual coefficient is 1
G = nx.tetrahedral_graph()
assert (average_clustering(G, trials=int(len(G) / 2)) ==
nx.average_clustering(G))
def basic_operation_tutorial():
# Create a graph.
G = nx.Graph()
# Nodes.
G.add_node(1)
G.add_nodes_from([2, 3])
H = nx.path_graph(10) # Creates a graph.
G.add_nodes_from(H)
G.add_node(H)
#print('G.nodes = {}.'.format(G.nodes))
print('G.nodes = {}.'.format(list(G.nodes)))
# Edges.
G.add_edge(1, 2)
e = (2, 3)
G.add_edge(*e) # Unpack edge tuple.
G.add_edges_from([(1, 2), (1, 3)])
G.add_edges_from(H.edges)
#print('G.edges = {}.'.format(G.edges))
print('G.edges = {}.'.format(list(G.edges)))
# Remove all nodes and edges.
G.clear()
#--------------------
G.add_edges_from([(1, 2), (1, 3)])
G.add_node(1)
G.add_edge(1, 2)
G.add_node('spam') # Adds node 'spam'.
G.add_nodes_from('spam') # Adds 4 nodes: 's', 'p', 'a', 'm'.
G.add_edge(3, 'm')
print('G.number_of_nodes() = {}.'.format(G.number_of_nodes()))
print('G.number_of_edges() = {}.'.format(G.number_of_edges()))
# Set-like views of the nodes, edges, neighbors (adjacencies), and degrees of nodes in a graph.
print('G.adj[1] = {}.'.format(list(G.adj[1]))) # or G.neighbors(1).
print('G.degree[1] = {}.'.format(
G.degree[1])) # The number of edges incident to 1.
# Report the edges and degree from a subset of all nodes using an nbunch.
# An nbunch is any of: None (meaning all nodes), a node, or an iterable container of nodes that is not itself a node in the graph.
print("G.edges([2, 'm']) = {}.".format(G.edges([2, 'm'])))
print('G.degree([2, 3]) = {}.'.format(G.degree([2, 3])))
# Remove nodes and edges from the graph in a similar fashion to adding.
G.remove_node(2)
G.remove_nodes_from('spam')
print('G.nodes = {}.'.format(list(G.nodes)))
G.remove_edge(1, 3)
# When creating a graph structure by instantiating one of the graph classes you can specify data in several formats.
G.add_edge(1, 2)
H = nx.DiGraph(G) # Creates a DiGraph using the connections from G.
print('H.edges() = {}.'.format(list(H.edges())))
edgelist = [(0, 1), (1, 2), (2, 3)]
H = nx.Graph(edgelist)
#--------------------
# Access edges and neighbors.
print('G[1] = {}.'.format(G[1])) # Same as G.adj[1].
print('G[1][2] = {}.'.format(G[1][2])) # Edge 1-2.
print('G.edges[1, 2] = {}.'.format(G.edges[1, 2]))
# Get/set the attributes of an edge using subscript notation if the edge already exists.
G.add_edge(1, 3)
G[1][3]['color'] = 'blue'
G.edges[1, 2]['color'] = 'red'
# Fast examination of all (node, adjacency) pairs is achieved using G.adjacency(), or G.adj.items().
# Note that for undirected graphs, adjacency iteration sees each edge twice.
FG = nx.Graph()
FG.add_weighted_edges_from([(1, 2, 0.125), (1, 3, 0.75), (2, 4, 1.2),
(3, 4, 0.375)])
for n, nbrs in FG.adj.items():
for nbr, eattr in nbrs.items():
wt = eattr['weight']
if wt < 0.5: print(f'({n}, {nbr}, {wt:.3})')
# Convenient access to all edges is achieved with the edges property.
for (u, v, wt) in FG.edges.data('weight'):
if wt < 0.5: print(f'({u}, {v}, {wt:.3})')
#--------------------
# Attributes.
# Graph attributes.
G = nx.Graph(day='Friday')
print('G.graph = {}.'.format(G.graph))
G.graph['day'] = 'Monday'
# Node attributes: add_node(), add_nodes_from(), or G.nodes.
G.add_node(1, time='5pm')
G.add_nodes_from([3], time='2pm')
print('G.nodes[1] = {}.'.format(G.nodes[1]))
G.nodes[1]['room'] = 714
print('G.nodes.data() = {}.'.format(G.nodes.data()))
print('G.nodes[1] = {}.'.format(
G.nodes[1])) # List the attributes of a node.
print('G.nodes[1].keys() = {}.'.format(G.nodes[1].keys()))
#print('G[1] = {}.'.format(G[1])) # G[1] = G.adj[1].
# Edge attributes: add_edge(), add_edges_from(), or subscript notation.
G.add_edge(1, 2, weight=4.7)
G.add_edges_from([(3, 4), (4, 5)], color='red')
G.add_edges_from([(1, 2, {'color': 'blue'}), (2, 3, {'weight': 8})])
G[1][2]['weight'] = 4.7
G.edges[3, 4]['weight'] = 4.2
print('G.edges.data() = {}.'.format(G.edges.data()))
print('G.edges[3, 4] = {}.'.format(
G.edges[3, 4])) # List the attributes of an edge.
print('G.edges[3, 4].keys() = {}.'.format(G.edges[3, 4].keys()))
#--------------------
# Directed graphs.
DG = nx.DiGraph()
DG.add_weighted_edges_from([(1, 2, 0.5), (3, 1, 0.75)])
print("DG.out_degree(1, weight='weight') = {}.".format(
DG.out_degree(1, weight='weight')))
print("DG.degree(1, weight='weight') = {}.".format(
DG.degree(
1, weight='weight'))) # The sum of in_degree() and out_degree().
print('DG.successors(1) = {}.'.format(list(DG.successors(1))))
print('DG.neighbors(1) = {}.'.format(list(DG.neighbors(1))))
# Convert G to undirected graph.
#H = DG.to_undirected()
H = nx.Graph(DG)
#--------------------
# Multigraphs: Graphs which allow multiple edges between any pair of nodes.
MG = nx.MultiGraph()
#MDG = nx.MultiDiGraph()
MG.add_weighted_edges_from([(1, 2, 0.5), (1, 2, 0.75), (2, 3, 0.5)])
print("MG.degree(weight='weight') = {}.".format(
dict(MG.degree(weight='weight'))))
GG = nx.Graph()
for n, nbrs in MG.adjacency():
for nbr, edict in nbrs.items():
minvalue = min([d['weight'] for d in edict.values()])
GG.add_edge(n, nbr, weight=minvalue)
print('nx.shortest_path(GG, 1, 3) = {}.'.format(nx.shortest_path(GG, 1,
3)))
#--------------------
# Classic graph operations:
"""
subgraph(G, nbunch): induced subgraph view of G on nodes in nbunch
union(G1,G2): graph union
disjoint_union(G1,G2): graph union assuming all nodes are different
cartesian_product(G1,G2): return Cartesian product graph
compose(G1,G2): combine graphs identifying nodes common to both
complement(G): graph complement
create_empty_copy(G): return an empty copy of the same graph class
to_undirected(G): return an undirected representation of G
to_directed(G): return a directed representation of G
"""
#--------------------
# Graph generators.
# Use a call to one of the classic small graphs:
petersen = nx.petersen_graph()
tutte = nx.tutte_graph()
maze = nx.sedgewick_maze_graph()
tet = nx.tetrahedral_graph()
# Use a (constructive) generator for a classic graph:
K_5 = nx.complete_graph(5)
K_3_5 = nx.complete_bipartite_graph(3, 5)
barbell = nx.barbell_graph(10, 10)
lollipop = nx.lollipop_graph(10, 20)
# Use a stochastic graph generator:
er = nx.erdos_renyi_graph(100, 0.15)
ws = nx.watts_strogatz_graph(30, 3, 0.1)
ba = nx.barabasi_albert_graph(100, 5)
red = nx.random_lobster(100, 0.9, 0.9)
#--------------------
# Read a graph stored in a file using common graph formats, such as edge lists, adjacency lists, GML, GraphML, pickle, LEDA and others.
nx.write_gml(red, './test.gml')
mygraph = nx.read_gml('./test.gml')
node_color='firebrick',
alpha=0.8,
)
#%%
#有向图
DG = nx.DiGraph()
DG.add_weighted_edges_from([(1, 2, 0.5), (3, 1, 0.75)])
print(DG.out_degree(1, weight='weight'))
print(DG.degree(1, weight='weight'))
print(list(DG.successors(1)))
print(list(DG.neighbors(1)))
#有向图和无向图的转换
#%%
#其他生成图的方法
petersen = nx.petersen_graph()
tutte = nx.tutte_graph()
maze = nx.sedgewick_maze_graph()
tet = nx.tetrahedral_graph()
K_5 = nx.complete_graph(5)
K_3_5 = nx.complete_bipartite_graph(3, 5)
barbell = nx.barbell_graph(10, 10)
lollipop = nx.lollipop_graph(10, 20)
#%%
plt.subplot(111)
nx.draw(K_3_5, with_labels=True, node_color='firebrick', alpha=0.8)
#%%
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 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)
# [1,2,3,4] GH6.edges() # [((2,3),(3,4)] # Retourne un graphe avec des aretes qui sont soit dans G soit dans H mais pas les deux ##### Graphes classiques ##### petersen=nx.petersen_graph() petersen.nodes() #[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] petersen.edges() #[(0, 1), (0, 4), (0, 5), (1, 2), (1, 6), (2, 3), (2, 7), (3, 8), (3, 4), (4, 9), (5, 8), (5, 7), (6, 8), (6, 9), (7, 9)] tutte=nx.tutte_graph() tutte.nodes() tutte.edges() maze=nx.sedgewick_maze_graph() maze.nodes() maze.edges() tet=nx.tetrahedral_graph() tet.nodes() #[0, 1, 2, 3] tet.edges() #[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)] #Remarque : il existe de nombreux generateurs de graphes