def test_is_eulerian(self):
assert_true(is_eulerian(nx.complete_graph(5)))
assert_true(is_eulerian(nx.complete_graph(7)))
assert_true(is_eulerian(nx.hypercube_graph(4)))
assert_true(is_eulerian(nx.hypercube_graph(6)))
assert_false(is_eulerian(nx.complete_graph(4)))
assert_false(is_eulerian(nx.complete_graph(6)))
assert_false(is_eulerian(nx.hypercube_graph(3)))
assert_false(is_eulerian(nx.hypercube_graph(5)))
assert_false(is_eulerian(nx.petersen_graph()))
assert_false(is_eulerian(nx.path_graph(4)))
def test_is_eulerian(self):
assert nx.is_eulerian(nx.complete_graph(5))
assert nx.is_eulerian(nx.complete_graph(7))
assert nx.is_eulerian(nx.hypercube_graph(4))
assert nx.is_eulerian(nx.hypercube_graph(6))
assert not nx.is_eulerian(nx.complete_graph(4))
assert not nx.is_eulerian(nx.complete_graph(6))
assert not nx.is_eulerian(nx.hypercube_graph(3))
assert not nx.is_eulerian(nx.hypercube_graph(5))
assert not nx.is_eulerian(nx.petersen_graph())
assert not nx.is_eulerian(nx.path_graph(4))
def test_is_eulerian2(self):
# not connected
G = nx.Graph()
G.add_nodes_from([1, 2, 3])
assert not nx.is_eulerian(G)
# not strongly connected
G = nx.DiGraph()
G.add_nodes_from([1, 2, 3])
assert not nx.is_eulerian(G)
G = nx.MultiDiGraph()
G.add_edge(1, 2)
G.add_edge(2, 3)
G.add_edge(2, 3)
G.add_edge(3, 1)
assert not nx.is_eulerian(G)
def test_is_eulerian2(self):
# not connected
G = nx.Graph()
G.add_nodes_from([1,2,3])
assert_false(is_eulerian(G))
# not strongly connected
G = nx.DiGraph()
G.add_nodes_from([1,2,3])
assert_false(is_eulerian(G))
G = nx.MultiDiGraph()
G.add_edge(1,2)
G.add_edge(2,3)
G.add_edge(2,3)
G.add_edge(3,1)
assert_false(is_eulerian(G))
def is_eulerian(self):
eulerian = nx.is_eulerian(self.graph)
print(self.graph)
if eulerian:
print("Graph is eulerian")
else:
print("Graph is not eulerian")
def get_eulerian(edict):
G = nx.DiGraph(edict)
if (not nx.is_eulerian(G)):
out_degrees = G.out_degree([node for node in G])
in_degrees = G.in_degree([node for node in G])
ds = [out_degrees, in_degrees]
d = {}
out_degree_dict = dict(out_degrees)
for k in out_degree_dict.keys():
d[k] = tuple(d[k] for d in ds)
for key in d:
d[key] = d[key][0] - d[key][1]
extra_out = [key for (key, value) in d.items() if value == 1][0]
extra_in = [key for (key, value) in d.items() if value == -1][0]
G.add_edge(extra_in, extra_out)
euler = list(nx.eulerian_circuit(G, source=extra_out))
index = euler.index((extra_in, extra_out))
blah = euler[index + 1:] + euler[:index]
path = []
path = blah[0][0] + sign + blah[0][1]
for line in blah[1:]:
path = path + (sign + line[1])
else:
eulerian = list(nx.eulerian_circuit(G))
path = eulerian[0][0] + sign + eulerian[0][1]
for line in eulerian[1:]:
path = path + (sign + line[1])
return path
def determine_combinations(self):
log.info('eulerian=%s, odd_ndoes=%s', nx.is_eulerian(self.g), len(self.odd_nodes))
odd_node_pairs = self.get_pair_combinations(self.odd_nodes)
log.info('combinations=%s', len(odd_node_pairs))
odd_pair_paths = self.get_shortest_path_pairs(self.g, odd_node_pairs)
# XXX - this part doesn't work well because it doesn't
# consider the direction of the paths.
# create another graph off odd pairs.. using negative weights
# because we want minimum distances but only maximum algorithm
# exists in networkx.
self.g_odd_nodes = nx.Graph()
for k, length in odd_pair_paths.items():
i,j = k
attrs = {
'length': length,
'weight': -length,
}
self.g_odd_nodes.add_edge(i, j, **attrs)
pass
log.info('new_nodes=%s, edges=%s, eulerian=%s', self.g_odd_nodes.order(), self.g_odd_nodes.size(), nx.is_eulerian(self.g_odd_nodes))
log.info('calculating max weight matching - this can also take a while')
return
def augment_graph(self, g, pairs):
# create a new graph and stuff in the new fake/virtual edges
# between odd pairs. Generate the edge metadata to make them
# look similar to the native edges.
graph_aug = g.copy()
log.info('(augmented) eulerian=%s', nx.is_eulerian(graph_aug))
for i, pair in enumerate(pairs):
a, b = pair
length, path = nx.single_source_dijkstra(g, a, b, weight='length')
log.debug('PAIR[%s] nodes = (%s,%s), length=%s, path=%s', i, a, b, length, path)
linestring = self.path_to_linestring(graph_aug, path)
# create a linestring of paths...
data = {
'length': length,
'augmented': True,
'path': path,
'geometry': linestring,
'from': a,
'to': b,
}
log.debug(' creating new edge (%s,%s) - data=%s', a, b, data)
graph_aug.add_edge(a, b, **data)
pass
return graph_aug
def pair_composition(pair_mers):
g = nx.DiGraph()
for kmer in pair_mers:
k1,k2 = kmer.split('|')
pre1 = k1[:-1]
pre2 = k2[:-1]
suf1 = k1[1:]
suf2 = k2[1:]
n1 = '%s,%s' % (pre1,pre2)
n2 = '%s,%s' % (suf1,suf2)
if n1 not in g:
g.add_node(n1)
if n2 not in g:
g.add_node(n2)
g.add_edge(n1, n2, label=kmer)
for n in g.nodes():
in_deg = len(g.predecessors(n))
out_deg = len(g.successors(n))
print 'node %s: in=%d, out=%d' % (n, in_deg, out_deg)
print 'Pair composition: is_eulerian=%d' % (nx.is_eulerian(g))
return g
def augment_graph(self, g, pairs):
graph_aug = g.copy()
log.info('(augmented) eulerian=%s', nx.is_eulerian(graph_aug))
for i, pair in enumerate(pairs):
a, b = pair
length, path = nx.single_source_dijkstra(g, a, b, weight='length')
log.debug('PAIR[%s] nodes = (%s,%s), length=%s, path=%s', i, a, b, length, path)
linestring = self.path_to_linestring(graph_aug, path)
# create a linestring of paths...
data = {
'length': length,
'augmented': True,
'path': path,
'geometry': linestring,
'from': a,
'to': b,
}
log.debug(' creating new edge (%s,%s) - data=%s', a, b, data)
graph_aug.add_edge(a, b, **data)
pass
return graph_aug
def euler_path2(graph: dict) -> list:
nx_graph = build_di_graph(graph)
edge = balance_graph(nx_graph)
if not nx.is_eulerian(nx_graph):
raise ValueError("Not Eulerian: {0}".format(graph))
return eulerian_cycle(build_dict_graph(nx_graph), edge[1])
def compute_features(self):
# checking if eulerian
self.add_feature(
"eulerian",
lambda graph: nx.is_eulerian(graph) * 1,
"A graph is eulerian if it has a eulerian circuit: a closed walk that includes \
each edges of the graph exactly once",
InterpretabilityScore(3),
)
# checking if semi eulerian
self.add_feature(
"semi_eulerian",
lambda graph: nx.is_semieulerian(graph) * 1,
"A graph is semi eulerian if it has a eulerian path but no eulerian circuit",
InterpretabilityScore(3),
)
# checking if eulerian path exists
self.add_feature(
"semi_eulerian",
lambda graph: nx.has_eulerian_path(graph) * 1,
"Whether a eulerian path exists in the network",
InterpretabilityScore(3),
)
def network_links_andEulerian_check():
'''For Eulerian cycle and path analyses'''
'''There are two parts to this function'''
'''Part 1 - Network construction and visualisation'''
# Network details
a = input('Give the name for your network : ')
b = (input('Enter the nodes for your network (separated by commas) : ')
).split(',')
c = int(input('How many links will your network have? '))
d = "Enter one link connecting two nodes in the following manner: For example, if linking 'A' to 'B', type, 'A' LINK 'B' : "
e = [list(input(d)) for _ in [0] * c]
f = []
# Processing of input data so that it is suitable for nx
for i in e:
g = (''.join(i)).replace('LINK'.upper(), ',')
f.append(g)
# Final pre-nx processing before transferring to nx for further handling
G = nx.Graph()
G.add_nodes_from(b)
for i in f:
eval("G.add_edge(" + i + ")")
nx.draw(G, with_labels=True)
plt.savefig(a + '.png')
plt.show()
'''Part 2 - Eulerian cycle and path analyses of network'''
# For the logic behind the code for the analyses, see the illustrations at:
# https://www.geeksforgeeks.org/eulerian-path-and-circuit/
h = G.degree(b)
j = []
for i in h:
if (i[1]) % 2 != 0: j.append(i[1])
if nx.is_eulerian(G) == True and len(j) == 0:
print('The network has a Eulerian cycle.')
elif nx.is_eulerian(G) == False and len(j) == 2:
print('The network has a Eulerian path.')
elif nx.is_eulerian(G) == False and (len(j) != 0 or len(j) != 2):
print('The network neither has a Eulerian path or Eulerian cycle.')
print(h)
def drow_war():
if nx.is_eulerian(G) == True:
warunki = Label(window, text="Warunek Eulera spełniony")
warunki.grid(row=5, column=4)
button_Eul.config(state="normal")
else:
warunki = Label(window, text="Warunek Eulera niespelniony")
warunki.grid(row=5, column=4)
def __init__(self, scaffold_graph):
print "Entering PathFinder module:", str(datetime.now())
self.G = scaffold_graph.copy()
#Build strandless list of sequences
sequences = set([n for n in self.G.nodes() if n > 0])
#Define weakly connected components
print "1... Defining weakly connected components"
component_graphs = set([g for g in nx.weakly_connected_component_subgraphs(self.G)])
single_node_graphs = set([g for g in component_graphs if len(g.nodes()) == 1])
multi_node_graphs = set([g for g in component_graphs if len(g.nodes()) > 1])
print "Number of single-node components:", len(single_node_graphs)
print "Number of multi-node components:", len(multi_node_graphs)
#Consolidate unscaffolded nodes, discard reverse strand
print "2... Consolidating single-node components"
unscaffolded = set([g.nodes()[0] for g in single_node_graphs])
discard_nodes = set([n for n in unscaffolded if n < 0])
for g in iter(single_node_graphs.copy()):
if g.nodes()[0] in discard_nodes:
single_node_graphs.discard(g)
print "Number of unscaffolded sequences:", len(single_node_graphs)
#Classify multi-node graphs
print "3... Classifying multi-node components"
DAG = set([])
Euler = set([])
for g in multi_node_graphs:
if nx.is_directed_acyclic_graph(g):
DAG.add(g)
elif nx.is_eulerian(g):
Euler.add(g)
else:
sys.exit("FATAL ERROR: Unknown multi-node graph type!")
print "Number of directed acyclic graphs:", len(DAG)
print "Number of Eulerian graphs:", len(Euler)
#Build scaffolds from DAGs
print "4... Building scaffolds from directed acyclic graphs"
self.scaffolds = set([])
for g in DAG:
self.build_dag_scaffold(g)
#Consolidating complementary scaffolds, keep first found
print "5... Consolidating complementary scaffolds"
consolidated_scaff = set([])
for seq in iter(self.scaffolds):
comp = self.revc(seq)
if comp in self.scaffolds:
if comp not in consolidated_scaff:
consolidated_scaff.add(seq)
else:
print "WARNING: non-complemented scaffold"
self.scaffolds = consolidated_scaff
print "Number of scaffolds assembled:", len(self.scaffolds)
#Build scaffolds from Eulerian graphs
#Add unscaffolded seqs to scaffolds list
print "6... Adding unscaffolded sequences to output"
for g in single_node_graphs:
seq = self.G.node[g.nodes()[0]]['seq']
self.scaffolds.add(seq)
print "Leaving PathFinder module:", str(datetime.now())
def euler_path(graph: nx.DiGraph, func=genome_path_string) -> list:
edge = balance_graph(graph)
if not nx.is_eulerian(graph):
raise ValueError("Not Eulerian: {0}".format(graph))
circuit = list(nx.eulerian_circuit(graph, edge[1]))
#print("asdf {0}".format(circuit))
#return [ func(x) for x in circuit ]
return [x[0] for x in circuit] + [ circuit[0][0] ]
def planning(self, ):
"""
"""
print('--------------------------------------------------')
print('(i) Make initial graph')
self.G = nx.Graph()
self.G = self.delaunay_network()
print('|V|=', self.G.number_of_nodes())
print('|E|=', self.G.number_of_edges())
# draw initial graph G
# nx.draw_networkx(self.G, pos=self.pos, ax=self.ax_G)
"""
"""
print('--------------------------------------------------')
print('(ii) Modify to be Eulerian')
self.Ge = nx.MultiGraph()
self.Ge, odd_nodes, M = self.chinese_postmap_problem(self.G)
print('|Ve|=', self.Ge.number_of_nodes())
print('|Ee|=', self.Ge.number_of_edges())
# draw odd nodes on G
nx.draw_networkx_nodes(
self.G,
pos=self.pos,
nodelist=odd_nodes,
node_color='r',
ax=self.ax_G,
)
# draw Eulerian graph Ge
# nx.draw_networkx_edges(self.G,
# pos=self.pos,
# edgelist=M,
# edge_color='r',
# ax=self.ax_G,)
if not nx.is_eulerian(self.Ge):
print('Not Eulerian')
sys.exit(-1)
eularian_circuit = list(nx.eulerian_circuit(self.Ge, 0))
print('Eularian circuit ==>')
print(eularian_circuit)
"""
"""
print('--------------------------------------------------')
print('(iii) Compute Hamiltonian circuit (way points)')
way_points = [self.h(e[0], e[1]) for e in eularian_circuit]
way_points = [[round(p[0], 2), round(p[1], 2)] for p in way_points]
way_points.append(way_points[0])
# print(way_points)
shift_way_points = way_points[1:] + way_points[:1]
L = 0.0
for i, j in zip(way_points, shift_way_points):
# print(i,j)
L = L + distance.euclidean(i, j)
print(L)
return way_points
def eulerian_path(edge_dict):
'''Generates an Eulerian cycle from the given edges.'''
G = nx.DiGraph(edge_dict)
if not (nx.is_eulerian(G)):
out_degrees = G.out_degree([node for node in G])
in_degrees = G.in_degree([node for node in G])
ds = [out_degrees, in_degrees]
d = {}
for k in out_degrees.keys():
d[k] = tuple(d[k] for d in ds)
for key in d:
d[key] = d[key][0] - d[key][1]
extra_out = [key for (key, value) in d.items() if value == 1][0]
extra_in = [key for (key, value) in d.items() if value == -1][0]
edge_dict[extra_in] = extra_out
current_node = extra_out
else:
current_node = next(iter(edge_dict.keys()))
path = [current_node]
# Get the initial cycle.
while True:
path.append(edge_dict[current_node][0])
if len(edge_dict[current_node]) == 1:
del edge_dict[current_node]
else:
edge_dict[current_node] = edge_dict[current_node][1:]
if path[-1] in edge_dict:
current_node = path[-1]
else:
break
# Continually expand the initial cycle until we're out of edge_dict.
while len(edge_dict) > 0:
for i in range(len(path)):
if path[i] in edge_dict:
current_node = path[i]
cycle = [current_node]
while True:
cycle.append(edge_dict[current_node][0])
if len(edge_dict[current_node]) == 1:
del edge_dict[current_node]
else:
edge_dict[current_node] = edge_dict[current_node][1:]
if cycle[-1] in edge_dict:
current_node = cycle[-1]
else:
break
path = path[:i] + cycle + path[i + 1:]
break
return path
def check_graph(graph, shape, max_stitch_length):
if networkx.is_empty(graph) or not networkx.is_eulerian(graph):
if shape.area < max_stitch_length**2:
message = "This shape is so small that it cannot be filled with rows of stitches. " \
"It would probably look best as a satin column or running stitch."
raise InvalidPath(_(message))
else:
message = "Cannot parse shape. " \
"This most often happens because your shape is made up of multiple sections that aren't connected."
raise InvalidPath(_(message))
def eulerian_path(G, source=None, keys=False):
"""Return an iterator over the edges of an Eulerian path in `G`.
Parameters
----------
G : NetworkX Graph
The graph in which to look for an eulerian path.
source : node or None (default: None)
The node at which to start the search. None means search over all
starting nodes.
keys : Bool (default: False)
Indicates whether to yield edge 3-tuples (u, v, edge_key).
The default yields edge 2-tuples
Yields
------
Edge tuples along the eulerian path.
Warning: If `source` provided is not the start node of an Euler path
will raise error even if an Euler Path exists.
"""
if not has_eulerian_path(G, source):
raise nx.NetworkXError("Graph has no Eulerian paths.")
if G.is_directed():
G = G.reverse()
if source is None or nx.is_eulerian(G) is False:
source = _find_path_start(G)
if G.is_multigraph():
for u, v, k in _multigraph_eulerian_circuit(G, source):
if keys:
yield u, v, k
else:
yield u, v
else:
yield from _simplegraph_eulerian_circuit(G, source)
else:
G = G.copy()
if source is None:
source = _find_path_start(G)
if G.is_multigraph():
if keys:
yield from reversed([
(v, u, k)
for u, v, k in _multigraph_eulerian_circuit(G, source)
])
else:
yield from reversed([
(v, u)
for u, v, k in _multigraph_eulerian_circuit(G, source)
])
else:
yield from reversed([
(v, u) for u, v in _simplegraph_eulerian_circuit(G, source)
])
def eulerian_Detector(self):
"""
Для неориентированного графа
if self._edges_value > 0:
graph = copy.deepcopy(self._edges) # Буферный граф
odd = [ vertex for vertex in graph.keys() if len(graph[vertex]) & 1 ]
keys = []
for key in graph.keys():
keys.append(key)
odd.append(keys[0])
if len(odd) > 3:
print("Граф не содержит Эйлерова цикла")
print("")
return
stack = [ odd[0] ]
path = []
# Цикл обхода графа
while stack:
vertex = stack[-1]
if graph[vertex]:
jertex = graph[vertex][0]
stack.append(jertex)
del graph[jertex][ graph[jertex].index(vertex) ]
del graph[vertex][0]
else:
path.append(stack.pop())
print("Эйлеров цикл в введенном графе: ")
print (str(path))
print("")
return path
else:
print("Граф пуст")
print("")
"""
# Для всех типов графов:
if self._edges_value > 0:
G = nx.DiGraph()
for vertex in self._edges.keys():
values = self._edges[vertex]
for value in values:
G.add_edge(vertex, value)
if nx.is_eulerian(G):
print("Граф содержит Эйлеров цикл")
print("Эйлеров цикл в введенном графе: ")
print (str(list(nx.eulerian_circuit(G))))
print("")
return list(nx.eulerian_circuit(G))
else:
print("Граф не содержит Эйлеров цикл")
print("")
else:
print("Граф пуст")
print("")
def find_eulerian_path_same_startend(graph, start):
''' Finds an eulerian path in the graph that returns to the starting point'''
if nx.is_eulerian(graph) == False:
print 'Graph is not eulerian, aborting'
return
eulerian_edge_path = nx.eulerian_circuit(graph, source=start)
path = []
for edge in eulerian_edge_path:
path.append(edge[0])
path.append(edge[1])
return path
def christofides(graph_x, subset_graph):
t0 = time.clock()
# ******* PHASE 1 ********
# Make graph_x complete with shortest path between nodes for missing edges
graph_comp = make_complete(subset_graph, graph_x)
new_edges = missing_edges(subset_graph)
simplified = simplify_complete(graph_comp,new_edges)
# ******* PHASE 2 *******
matching_edges = match_components(subset_graph, simplified, graph_x)
# Add component matching edges to Gr
subset_plus_comp = subset_graph.copy()
for edge in matching_edges:
subset_plus_comp.add_weighted_edges_from([(edge[0],edge[1],
simplified[edge[0]][edge[1]]['weight'])])
perfect_matching = call_blossom(subset_plus_comp,graph_x)
final = nx.MultiGraph(subset_plus_comp)
for edge in perfect_matching:
# If edge exists in original graph:
if graph_x.has_edge(*edge):
final.add_weighted_edges_from([(edge[0],edge[1],
graph_x[edge[0]][edge[1]]['weight'])])
# Else get shortest path between them and replace
else:
final.add_weighted_edges_from(shortest_path_edges(edge[0],edge[1],graph_x))
if nx.is_eulerian(final):
tour = list(nx.eulerian_circuit(final))
t1 = time.clock()
results = list()
results.append(tour_cost(tour, graph_comp))
runtime = t1 - t0
results.append(runtime)
results.append(tour_cost(tour, graph_comp))
results.append(runtime)
results.append(check_solution(tour,graph_x,subset_graph))
print(tour)
print(results)
else:
results = list()
t1 = time.clock()
results.append(0)
runtime = t1 - t0
results.append(runtime)
results.append(0)
results.append(runtime)
results.append(False)
return results
def circuito_euleriano(graph):
G = None
# print("graph é euleriano? ", nx.is_eulerian(graph))
if not nx.is_eulerian(graph):
G = eulerize(graph)
circuito = list(nx.eulerian_circuit(G))
nos = []
for u, v in circuito:
nos.append(u)
nos.append(circuito[0][0])
return nos
def UndirectedGraphFeature(df, dfOrigin, part):
indexs, files = df.index, dfOrigin.file_id.unique()
for col in apiSet:
df[col+'_center_degree'] = 0
for index, file in zip(indexs, files):
X = pd.read_csv('./' + part + '/' + str(index) + '.csv')
api = X.groupby(by='tid').apply(lambda x: ' '.join(x.api))
api = pd.DataFrame(api)
api.rename(columns={0: 'api_call'}, inplace=True)
G = nx.Graph()
for row in api.index:
apiCall = (api.loc[row, 'api_call']).split(' ')
for i in range(len(apiCall) - 1):
G.add_edge(apiCall[i], apiCall[i + 1])
if (len(G) <= 1):
continue
isConnnected = (nx.is_connected(G) == False)
if isConnnected:
df.loc[index, 'avg_length'] = -1
df.loc[index, 'minimum_edge_cut'] = -1
df.loc[index, 'degree_assortativity_coefficient'] = -1
df.loc[index, 'radius'] = -1
df.loc[index, 'diameter'] = -1
df.loc[index, 'periphery'] = -1
df.loc[index, 'is_eulerian'] = -1
df.loc[index, 'center'] = -1
df.loc[index, 'order'] = -1
df.loc[index, 'size'] = -1
df.loc[index, 'density'] = -1
else:
df.loc[index, 'avg_length'] = nx.average_shortest_path_length(G)
df.loc[index, 'minimum_edge_cut'] = len(set(nx.minimum_edge_cut(G)))
df.loc[index, 'degree_assortativity_coefficient'] = nx.degree_assortativity_coefficient(G)
df.loc[index, 'radius'] = nx.radius(G)
df.loc[index, 'diameter'] = nx.diameter(G)
df.loc[index, 'periphery'] = len(set(nx.periphery(G)))
df.loc[index, 'is_eulerian'] = int(nx.is_eulerian(G))
df.loc[index, 'center'] = len(set(nx.center(G)))
df.loc[index, 'density'] = nx.density(G)
df.loc[index, 'order'] = G.order()
df.loc[index, 'size'] = G.size()
if not isConnnected:
for x in set(nx.center(G)):
df.loc[index,x+'_center_degree'] = 1
print(index)
return df
def determine_combinations(self):
log.info('eulerian=%s, odd_nodes=%s', nx.is_eulerian(self.g),
len(self.odd_nodes))
odd_node_pairs = self.get_pair_combinations(self.odd_nodes)
log.info('combinations=%s', len(odd_node_pairs))
odd_pair_paths = self.get_shortest_path_pairs(self.g, odd_node_pairs)
# XXX - this part doesn't work well because it doesn't
# consider the direction of the paths.
# create a temporary graph of odd pairs.. really we should be
# doing the combination max calculations here.
self.g_odd_nodes = nx.Graph()
for k, length in odd_pair_paths.items():
i, j = k
attrs = {
'length': length,
'weight': -length,
}
self.g_odd_nodes.add_edge(i, j, **attrs)
pass
log.info('new_nodes=%s, edges=%s, eulerian=%s',
self.g_odd_nodes.order(), self.g_odd_nodes.size(),
nx.is_eulerian(self.g_odd_nodes))
log.info(
'calculating max weight matching - this can also take a while')
return
def main():
genome = 'ATGGCGTGCA'
kmers = []
k = 3
for i in range(len(genome) - k + 1):
kmers.append(genome[i:i+k])
Graph = nx.DiGraph()
for i in kmers:
Graph.add_edge(i[0:2], i[1:3])
nx.draw(Graph)
plt.show()
for i in Graph.nodes():
if Graph.in_degree(i) != Graph.out_degree(i):
print "Node %s is unbalanced" % i
if Graph.in_degree(i) - Graph.out_degree(i) == 1:
end = i
print "Node %s is the End node" % i
if Graph.in_degree(i) - Graph.out_degree(i) == -1:
start = i
print "Node %s is the Start node" % i
print "Is this Graph Eulerian ? - %s" % nx.is_eulerian(Graph)
Graph.add_edge(end, start)
print "I have made some changes, is this Graph Eulerian now ? - %s" % nx.is_eulerian(Graph)
MaxOutDegree = -1
for i in Graph.nodes():
MaxOutDegree = Graph.out_degree(i) if Graph.out_degree(i) > MaxOutDegree else -1
paths = []
while len(paths) < MaxOutDegree:
temp = []
TempGraph = Graph.copy()
path = FindEulerianCycles(TempGraph, start, temp, end)
if path not in paths and len(path) > 0:
paths.append(path)
print paths
def euler(Graph): global start global finish find_balance(Graph) path=[] if nx.is_eulerian(Graph): circuit=list(nx.eulerian_circuit(Graph, start)) for edge in circuit: current=Graph.edge[edge[0]][edge[1]]['label'] if current != None: path.append(current) if unbalanced==0: finish=circuit.pop()[1] answer=start, path, finish print answer else: none()
def determine_circuit(self):
odd_matching = nx.algorithms.max_weight_matching(self.g_odd_nodes, True)
log.info('len(odd_matching)=%s', len(odd_matching))
log.debug('odd_matching=%s', odd_matching)
log.info('augment original')
self.g_augmented = self.augment_graph(self.g, odd_matching)
start_node = self.get_start_node(self.g, self.start)
log.info('(augmented) eulerian=%s', nx.is_eulerian(self.g_augmented))
self.euler_circuit = list(nx.eulerian_circuit(self.g_augmented, source=start_node))
return
def write_graph_info_to_file(G, graph_name=GRAPH_NAME):
with open("{}_info".format(graph_name), "w") as report_file:
try:
report_file.write("Number of nodes: {}\n".format(
G.number_of_nodes()))
report_file.write("Number of edges: {}\n".format(
G.number_of_edges()))
write_components_info(G, report_file)
write_distance_info(G, report_file)
write_dag_info(G, report_file)
report_file.write("Is Eulerian: {}\n".format(nx.is_eulerian(G)))
report_file.write("Density: {}\n".format(nx.density(G)))
report_file.write("Flow hierarchy: {}\n".format(
nx.flow_hierarchy(G)))
report_file.write("----INFO FROM NETWORKX----\n")
report_file.write("{}\n".format(nx.info(G)))
except ZeroDivisionError as e:
report_file.write("Zero Division: {}".format(e))
def euler_circ(self, graphe):
"""
Cette fonction prend en paramètre un graphe et retourne un tuple constitué de la liste d'aretes et
la liste de sommets dans l'ordre de parcours du circuit euleurien; ou -1 si le graphe n'est euleurian.
:param netW:
:param graphe:
:return:
"""
if nx.is_eulerian(graphe):
aretes_euler = list(nx.eulerian_circuit(graphe))
sommets_euler = [aretes_euler[0][0]]
for arete in aretes_euler:
for sommet in arete:
if sommet != sommets_euler[-1]:
sommets_euler.append(sommet)
return aretes_euler, sommets_euler
else:
return -1, -1
def find_euler_tour(self, nx_euler=False):
h = nx.MultiGraph()
h.add_edges_from(self.mst.edges())
h.add_edges_from(self.m.edges())
if not nx.is_eulerian(h):
raise ValueError('h must be eulerian')
print "find euler tour"
t1 = time.time()
if nx_euler:
euler_edges = nx.eulerian_circuit(h)
self.euler_path = [e for e in euler_edges]
else:
self.euler_path = self.build_euler_tour(h)
t2 = time.time()
print "took %s" % (t2 - t1)
print "euler path: ", self.euler_path
print '#edges:', len(self.euler_path), '#nodes:', len(h.nodes())
self.plot_edges(self.euler_path, 'c--', 2)
self.h = h
def find_euler_tour(self, nx_euler=False):
h = nx.MultiGraph()
h.add_edges_from(self.mst.edges())
h.add_edges_from(self.m.edges())
if not nx.is_eulerian(h):
raise ValueError('h must be eulerian')
print "find euler tour"
t1 = time.time()
if nx_euler:
euler_edges = nx.eulerian_circuit(h)
self.euler_path = [e for e in euler_edges]
else:
self.euler_path = self.build_euler_tour(h)
t2 = time.time()
print "took %s" % (t2-t1)
print "euler path: ", self.euler_path
print '#edges:', len(self.euler_path), '#nodes:', len(h.nodes())
self.plot_edges(self.euler_path,'c--',2)
self.h = h
def compute(cls, graph: nx.Graph, depot_index: int):
"""
:param graph: the graph where compute the TSP tour
:param: depot_index : the index of node which is referred as depot (start and end of the tour)
:return: the tsp Tour [e1,e2,...,en] with e1 with indexes of graph
"""
graph = graph.copy()
# first step -> MST of graph
mst = nx.minimum_spanning_tree(graph)
# even
odd_nodes = Christofides.odd_nodes(mst)
# induced subgraph of odd nodes
odd_graph = graph.subgraph(odd_nodes).copy()
# minimum weighted matching
perfect_match = Christofides.min_weight_matching(odd_graph)
# build Eulerian Graph: mst + perfect match
eu_graph = nx.MultiGraph()
for e0, e1 in list(mst.edges) + list(perfect_match):
eu_graph.add_node(e0, pos=graph.nodes[e0]["pos"])
eu_graph.add_node(e1, pos=graph.nodes[e1]["pos"])
eu_graph.add_edge(e0, e1, weight=graph.edges[e0, e1]["weight"])
# Assert a eulerian graph
assert nx.is_eulerian(
eu_graph
), "The mst + perfect matching of Christofides -> not an eulerian graph "
# eulerian tour
eu_tour = list(
nx.eulerian_circuit(eu_graph, source=depot_index, keys=False))
# shortcut tour to have a 1.5-TSP
tsp_tour = Christofides.shorted_tour(eu_tour)
return tsp_tour
def travelingSalesman(G, vertices, start):
"""
Christofides' algorithm to approximate tsp
"""
vertices = vertices[:]
vertices = list(set(sorted(vertices)))
mst_edges = MST(G, vertices)
mst_graph = nx.MultiGraph()
mst_graph.add_nodes_from(vertices)
mst_graph.add_edges_from(mst_edges)
O = []
for v in vertices:
if mst_graph.degree(v) % 2 == 1:
O.append(v)
m = G.subgraph(O).copy()
for u, v, data in m.edges(data=True):
data['weight'] *= -1
P = nx.algorithms.matching.max_weight_matching(m,
maxcardinality=True,
weight="weight")
for u, v in P:
a = len(mst_graph.edges())
mst_graph.add_edge(u, v, weight=getWeight(G, u, v))
ret = []
seen = set()
assert nx.is_eulerian(mst_graph)
for u, v in nx.eulerian_circuit(mst_graph, source=start):
if u not in seen:
ret.append(u)
seen.add(u)
ret.append(start)
return ret
def print_is_of_type_attrs(graph):
print("\n====== is of type X? ======")
print("Directed? ->", "Yes" if nx.is_directed(graph) else "No")
print("Directed acyclic? ->", "Yes" if nx.is_directed_acyclic_graph(graph) else "No")
print("Weighted? ->", "Yes" if nx.is_weighted(graph) else "No")
if nx.is_directed(graph):
print("Aperiodic? ->", "Yes" if nx.is_aperiodic(graph) else "No")
print("Arborescence? ->", "Yes" if nx.is_arborescence(graph) else "No")
print("Weakly Connected? ->", "Yes" if nx.is_weakly_connected(graph) else "No")
print("Semi Connected? ->", "Yes" if nx.is_semiconnected(graph) else "No")
print("Strongly Connected? ->", "Yes" if nx.is_strongly_connected(graph) else "No")
else:
print("Connected? ->", "Yes" if nx.is_connected(graph) else "No")
print("Bi-connected? ->", "Yes" if nx.is_biconnected(graph) else "No")
if not graph.is_multigraph():
print("Chordal? -> ", "Yes" if nx.is_chordal(graph) else "No")
print("Forest? -> ", "Yes" if nx.is_chordal(graph) else "No")
print("Distance regular? -> ", "Yes" if nx.is_distance_regular(graph) else "No")
print("Eulerian? -> ", "Yes" if nx.is_eulerian(graph) else "No")
print("Strongly regular? -> ", "Yes" if nx.is_strongly_regular(graph) else "No")
print("Tree? -> ", "Yes" if nx.is_tree(graph) else "No")
print("Standard Deviation of Node Degree: {0:.2}".format(standardDeviation))
###Displaying probability distribution of Node Degree
plt.figure(4)
plt.title('Node Degree Histogram of Undirected Graph')
plt.hist(ug.degree, bins=100)
# Part A: Analysis of Connected Components
print("The Amount of Connected Components: ",
nx.number_connected_components(ug))
ccs = [
len(c) for c in sorted(nx.connected_components(ug), key=len, reverse=True)
]
print("Largest Connected Component: ", ccs[0])
print("Smallest Connected Component: ", ccs[-1])
# Part E: Euler Network
print("Is subnetwork 1 Eularian? ", nx.is_eulerian(separate1))
print("Is subnetwork 2 Eularian? ", nx.is_eulerian(separate2))
# Part H: Minimum Spanning tree of network (ug) and largest CC (separate1)
a = nx.minimum_spanning_tree(ug)
print("Is tree?", nx.is_tree(a))
print("Is forest?", nx.is_forest(a))
separate1.remove_edge(3, 11)
b = nx.minimum_spanning_tree(separate1)
print("Removed edge from largest CC")
print("Is tree?", nx.is_tree(b))
print("Is forest?", nx.is_forest(b))
flName = 'moreno_highschool\README.moreno_highschool'
f = open(flName, 'r')
lines = f.readlines()
import networkx as nx
G = nx.Graph()
G.add_edges_from([(1, 2), (1, 3), (2, 3), (2, 4), (2, 6), (3, 4), (3, 5),
(4, 5), (4, 6), (5, 6), (5, 7), (6, 7)])
posicoes = {
1: (.5, 1),
2: (0, .75),
3: (1, .75),
4: (.5, .5),
5: (1, .25),
6: (0, .25),
7: (.5, 0),
}
nx.draw_networkx(G, pos=posicoes)
print("Grafo G")
print("-------")
print("É Euleriano?", "Sim" if nx.is_eulerian(G) else "Não")
print("É Semieuleriano?", "Sim" if nx.is_semieulerian(G) else "Não")
print("É Tem caminho Euliriano?", "Sim" if nx.has_eulerian_path(G) else "Não")
def test_on_eulerian_multigraph(self):
G = nx.MultiGraph(nx.cycle_graph(3))
G.add_edge(0, 1)
H = nx.eulerize(G)
assert_true(nx.is_eulerian(H))
def is_eulerian(g, **kwargs):
return nx.is_eulerian(g)
def find_eulerian_path(G):
"""Returns the edges of an Eulerian path in G, (if it exits).
An Eulerian path is a path that crosses every edge in G
exactly once.
Parameters
----------
G: NetworkX Graph, DiGraph, MultiGraph or MultiDiGraph
A directed or undirected Graph or MultiGraph.
Returns
-------
edges: generator
A generator that produces edges in the Eulerian path.
Raises
------
NetworkXError: If the graph does not have an eulerian path.
Notes
-----
Linear time algorithm, adapted from [1]_ and [3]_.
Information about euler paths in [2]_.
Code for eulerian circuit in [3]_.
Important: In [1], euler path is in reverse order,
this implementation gives the path in correct order
as in [3]_ for eulerian_circuit. The distinction for
directed graph is in using the in_degree neighbors, not the out
ones. for undirected, it is using itemgetter(1) for get_vertex,
which uses the correct vertex for this order. Also, every graph
has an even number of odd vertices by the Handshaking Theorem [4]_.
References
----------
.. [1] http://www.graph-magics.com/articles/euler.php
.. [2] http://en.wikipedia.org/wiki/Eulerian_path
.. [3] https://github.com/networkx/networkx/blob/master/networkx/algorithms/euler.py
.. [4] https://www.math.ku.edu/~jmartin/courses/math105-F11/Lectures/chapter5-part2.pdf
Examples
--------
>>> G = nx.Graph([('W', 'N'), ('N', 'E'), ('E', 'W'), ('W', 'S'), ('S', 'E')])
>>> list(nx.find_eulerian_path(G))
[('W', 'N'), ('N', 'E'), ('E', 'W'), ('W', 'S'), ('S', 'E')]
>>> G = nx.Digraph([(1, 2), (2, 3)])
>>> list(nx.find_eulerian_path(G))
[(1,2),(2,3)]
"""
from operator import itemgetter
# Verify that graph is connected, short circuit
if G.is_directed() and not nx.is_weakly_connected(G):
raise nx.NetworkXError("G is not connected.")
# is undirected
if not G.is_directed() and not nx.is_connected(G):
raise nx.NetworkXError("G is not connected.")
# Now verify if has an eulerian circuit:
# even condition of all nodes is satified.
if nx.is_eulerian(G):
x = nx.eulerian_circuit(G) # generator of edges
for i in x:
yield i
# Not all vertex have even degree,
# check if exactly two vertex have odd degrees.
# If yes, then there is an Euler path. If not,
# raise an error (no euler path can be found)
else:
g = G.__class__(G) # copy graph structure (not attributes)
# list to check the odd degree condition, and a flag
check_odd = []
directed = False
if g.is_directed():
degree = g.in_degree
out_degree = g.out_degree
edges = g.in_edges_iter
get_vertex = itemgetter(0)
directed = True
else:
degree = g.degree
edges = g.edges_iter
get_vertex = itemgetter(1)
# Verify if an euler path can be found. Complexity O(n) ?
for vertex in g.nodes():
deg = degree(vertex)
# directed case
if directed:
outdeg = out_degree(vertex)
if deg != outdeg:
# if we have more than 2 odd nodes,
# we do a raise (no euler path)
if len(check_odd) > 2:
raise nx.NetworkXError("G doesn't have an Euler Path.")
# is odd and we append it.
else:
check_odd.append(vertex)
# undirected case
else:
if deg % 2 != 0:
# if we have more than 2 odd nodes,
# we do a raise (no euler path)
if len(check_odd) > 2:
raise nx.NetworkXError("G doesn't have an Euler Path.")
# is odd and we append it.
else:
check_odd.append(vertex)
if directed:
def verify_odd_cond(g, check_odd):
first = check_odd[0]
second = check_odd[1]
if (g.out_degree(first) == g.in_degree(first) + 1 and
g.in_degree(second) == g.out_degree(second) + 1):
return second
elif (g.out_degree(second) == g.in_degree(second) + 1 and
g.in_degree(first) == g.out_degree(first) + 1):
return first
else:
return None
start = verify_odd_cond(g, check_odd)
else:
start = check_odd[0]
# if the odd condition is not meet, raise an error.
if not start:
raise nx.NetworkXError("G doesn't have an Euler Path.")
# Begin algorithm:
vertex_stack = [start]
last_vertex = None
while vertex_stack:
current_vertex = vertex_stack[-1] # (4)
# if no neighbors:
if degree(current_vertex) == 0:
# Special case, we cannot add a None vertex to the path.
if last_vertex is not None:
yield (last_vertex, current_vertex)
last_vertex = current_vertex
vertex_stack.pop()
# we have neighbors, so add the vertex to the stack (2),
# take any of its neighbors (1)
# remove the edge between selected neighbor and that vertex,
# and set that neighbor as the current vertex (4).
else:
random_edge = next(edges(current_vertex)) # (1)
vertex_stack.append(get_vertex(random_edge)) # (2)
g.remove_edge(*random_edge) # (3)
def test_on_complete_graph(self):
G = nx.complete_graph(4)
assert_true(nx.is_eulerian(nx.eulerize(G)))
assert_true(nx.is_eulerian(nx.eulerize(nx.MultiGraph(G))))
import matplotlib.pyplot as plt
from PIL import Image
from os import system
#G = nx.complete_graph(5)
G = nx.MultiGraph()
#G.add_nodes_from(["C", "A", "D", "B"])
#G.add_edges_from([{"C","A"}, {"C","A"}, {"A","B"}, {"A","B"}, {"C", "D"}, {"A", "D"}, {"B", "D"}])
G.add_edges_from([("C","A"), ("C","A"), ("A","B"), ("A","B"), ("C", "D"), ("A", "D"), ("B", "D")])
#G.add_edges_from([("C","A"), ("A","B"), ("C", "D"), ("A", "D"), ("B", "D")])
#G.add_edges_from([("C","A"), ("C","A"), ("A","B"), ("A","B"), ("C", "D"), ("A", "D"), ("B", "D"), ("A", "C"), ("B", "D")])
print("Nodes:", G.nodes())
print("Edges:", G.edges())
print("Nodes:", ", ".join(sorted(G.nodes())))
print("Edges:", ", ".join(sorted("{{{}}}".format(",".join(sorted(t))) for t in G.edges())))
print("The graph {} Eulerian.".format("is" if nx.is_eulerian(G) else "is not"))
spt = nx.minimum_spanning_edges(G, data=False)
print(list(spt))
#print("Edges:", ", ".join(sorted("{{{}}}".format(",".join(sorted(t))) for t in spt)))
#nx.set_node_attributes(G, "pos", {"C": { "pos": (0,2) }, "A": { "pos": (0,1) }, "D": { "pos": (1,0) }, "B": (0,0)})
#nx.draw_networkx(G, pos={"C": (0,2), "A": (0,1), "D": (1,0), "B": (0,0)})
#plt.axis("off")
#plt.show()
#nx.write_dot(G, "konigsberg.dot")
#system("circo -T png konigsberg.dot > konigsberg.png")
#img = Image.open('konigsberg.png')
#img.show()
membership[n.organism] = []
membership[n.organism].append([n.name, i+1])
print '\nHistogram of component order'
print 'order\tcount'
for n in sorted(sg_order_hist):
print '{0}\t{1}'.format(n, sg_order_hist[n])
print 'Writing subgraph info table.'
with open(args.output[0] + '.subgraph', 'w') as subinfo_h:
subinfo_wr = csv.writer(subinfo_h, delimiter='\t')
subinfo_wr.writerow(['id', 'size', 'order', 'density', 'eularian', 'binconn', 'modularity'])
for i, sg in enumerate(subgraphs):
part = com.best_partition(sg)
subinfo_wr.writerow([i+1, sg.size(), sg.order(), nx.density(sg),
nx.is_eulerian(sg), nx.is_biconnected(sg), com.modularity(part, sg)])
if args.writesubs:
print 'Writing all subgraphs ...'
for i, sg in enumerate(subgraphs):
out = os.path.join(args.work_dir[0], 'og{0}.graphml'.format(i+1))
nx.write_graphml(sg, out)
iso_count = 0
for org in membership:
print 'There remained {0} isolate genes in {1}'.format(len(isolate_genes[org]), org)
with open(org + '.memb', 'w') as memb_h:
memb_wr = csv.writer(memb_h, delimiter='\t')
memb_wr.writerow(['gene','og'])
for gn in membership[org]:
memb_wr.writerow(gn)
found = 0
for n in G.nodes_iter():
if G.in_degree(n) > G.out_degree(n):
n1 = n
found +=1
if G.out_degree(n) > G.in_degree(n):
n2 = n
found +=1
if found>=2:
break
G.add_edge(n1,n2)
print n2 + "->" + n1
if nx.is_eulerian(G):
nodes = []
temp_nodes = []
start = False
for u,v in nx.eulerian_circuit(G,source=n1):
if (u == n1) and (v == n2):
start = True
if start:
nodes.append(v)
else:
temp_nodes.append(v)
nodes += temp_nodes
print >>out, "->".join(str(n) for n in nodes)
print >> sys.stderr, "Finished!"
else:
print "Not Eulerian"
def main():
"""The main function.
Returns:
None
"""
G = nx.Graph()
G.add_edges_from((
('せんし', 'とうぞく', dict(skill='ぬすっと斬り')),
('せんし', 'おどりこ', dict(skill='つるぎのまい')),
('せんし', 'ぎんゆうしじん', dict(skill='たたかいの歌')),
('せんし', 'ふなのり', dict(skill='かもめ返し')),
('せんし', 'ひつじかい', dict(skill='みねうち')),
('せんし', 'わらわせし', dict(skill='へんてこ斬り')),
('ぶとうか', 'まほうつかい', dict(skill='火の息')),
('ぶとうか', 'とうぞく', dict(skill='きゅうしょ突き')),
('ぶとうか', 'おどりこ', dict(skill='マッスルダンス')),
('ぶとうか', 'ぎんゆうしじん', dict(skill='おたけび')),
('ぶとうか', 'ふなのり', dict(skill='すいめんげり')),
('ぶとうか', 'ひつじかい', dict(skill='マトンアタック')),
('ぶとうか', 'わらわせし', dict(skill='しっぺ返し')),
('まほうつかい', 'ぶとうか', dict(skill='火の息')),
('まほうつかい', 'とうぞく', dict(skill='マホトラ')),
('まほうつかい', 'おどりこ', dict(skill='マホキテ')),
('まほうつかい', 'ぎんゆうしじん', dict(skill='のろいの歌')),
('まほうつかい', 'ふなのり', dict(skill='いなずま')),
('まほうつかい', 'ひつじかい', dict(skill='ラリホーマ')),
('まほうつかい', 'わらわせし', dict(skill='メダパニ')),
('そうりょ', 'おどりこ', dict(skill='死のおどり')),
('そうりょ', 'ぎんゆうしじん', dict(skill='やすらぎの歌')),
('そうりょ', 'ふなのり', dict(skill='ノアのはこぶね')),
('そうりょ', 'ひつじかい', dict(skill='スクルト')),
('とうぞく', 'せんし', dict(skill='ぬすっと斬り')),
('とうぞく', 'ぶとうか', dict(skill='きゅうしょ突き')),
('とうぞく', 'まほうつかい', dict(skill='マホトラ')),
('とうぞく', 'おどりこ', dict(skill='マホトラおどり')),
('とうぞく', 'わらわせし', dict(skill='しのび笑い')),
('おどりこ', 'せんし', dict(skill='つるぎのまい')),
('おどりこ', 'ぶとうか', dict(skill='マッスルダンス')),
('おどりこ', 'まほうつかい', dict(skill='マホキテ')),
('おどりこ', 'そうりょ', dict(skill='死のおどり')),
('おどりこ', 'とうぞく', dict(skill='マホトラおどり')),
('おどりこ', 'ふなのり', dict(skill='船上ダンス')),
('おどりこ', 'ひつじかい', dict(skill='ひつじのダンス')),
('おどりこ', 'わらわせし', dict(skill='ステテコダンス')),
('ぎんゆうしじん', 'せんし', dict(skill='たたかいの歌')),
('ぎんゆうしじん', 'ぶとうか', dict(skill='おたけび')),
('ぎんゆうしじん', 'まほうつかい', dict(skill='のろいの歌')),
('ぎんゆうしじん', 'そうりょ', dict(skill='やすらぎの歌')),
('ぎんゆうしじん', 'ふなのり', dict(skill='さざなみの歌')),
('ぎんゆうしじん', 'ひつじかい', dict(skill='ひつじかぞえ歌')),
('ぎんゆうしじん', 'わらわせし', dict(skill='コミックソング')),
('ふなのり', 'せんし', dict(skill='かもめ返し')),
('ふなのり', 'ぶとうか', dict(skill='すいめんげり')),
('ふなのり', 'まほうつかい', dict(skill='いなずま')),
('ふなのり', 'そうりょ', dict(skill='ノアのはこぶね')),
('ふなのり', 'おどりこ', dict(skill='船上ダンス')),
('ふなのり', 'ぎんゆうしじん', dict(skill='さざなみの歌')),
('ひつじかい', 'せんし', dict(skill='みねうち')),
('ひつじかい', 'ぶとうか', dict(skill='マトンアタック')),
('ひつじかい', 'まほうつかい', dict(skill='ラリホーマ')),
('ひつじかい', 'そうりょ', dict(skill='スクルト')),
('ひつじかい', 'おどりこ', dict(skill='ひつじのダンス')),
('ひつじかい', 'ぎんゆうしじん', dict(skill='ひつじかぞえ歌')),
('わらわせし', 'せんし', dict(skill='へんてこ斬り')),
('わらわせし', 'ぶとうか', dict(skill='しっぺ返し')),
('わらわせし', 'まほうつかい', dict(skill='メダパニ')),
('わらわせし', 'とうぞく', dict(skill='しのび笑い')),
('わらわせし', 'おどりこ', dict(skill='ステテコダンス')),
('わらわせし', 'ぎんゆうしじん', dict(skill='コミックソング')),
#('けんじゃ', 'スーパースター', dict(skill='メガザルダンス')),
))
if nx.is_eulerian(G):
print_cycle(G)
G.remove_edge('ぎんゆうしじん', 'ぶとうか')
G.remove_edge('まほうつかい', 'とうぞく')
print_cycle(G, source='まほうつかい')