def random_graph(node_number,
edge_density,
seed=None,
is_tree=False,
plot=False):
if seed is not None:
graph = nx.random_tree(node_number, seed=seed)
else:
graph = nx.random_tree(node_number)
if not is_tree:
counter = 0
if seed is not None:
random.seed(seed)
while 1 + counter / graph.number_of_nodes() < edge_density:
v = random.randint(0, graph.number_of_nodes() - 1)
w = random.randint(0, graph.number_of_nodes() - 1)
if w != v and not graph.has_edge(v, w):
graph.add_edge(v, w)
counter += 1
if plot:
pos = graphviz_layout(graph, prog='neato')
nx.draw(graph, pos)
nx.draw_networkx_labels(graph, pos, nodelist=graph.nodes())
matplotlib.pyplot.show()
return graph
def r_tree(nodes, height=None):
'''
Generates a random tree, with random utility and demand for each node
:param nodes: Number of nodes in the tree
:param height: (optional) produces tree with given height.
:return: Random tree with len{V} = nodes
'''
G = nx.random_tree(nodes)
if height is not None:
while calc_height(G, get_root(G)) is not height:
G = nx.random_tree(nodes)
utils = {}
demand = {}
# for a given node, income = util - demand
income = {}
# random utils and demand for each node
for node in G.nodes:
utils.update({node: random.randint(1, 4)})
demand.update({node: random.randint(1, 2)})
income.update({node: utils[node] - demand[node]})
nx.set_node_attributes(G, name='util', values=utils)
nx.set_node_attributes(G, name='demand', values=demand)
nx.set_node_attributes(G, name='income', values=income)
return G
def generate_random_graph(n_nodes,
density,
directed=False,
is_tree=False,
seed=None,
draw=False):
r"""Generate a random graph with the desired number of nodes and density.
Draw the graph if asked. Returns the graph as a networkx object.
Parameters:
----------
n_nodes: int,
number of nodes
density: float (\in [0,1]),
density of edges
directed: bool,
whether or not the graph is directed
is_tree: bool,
whether to generate a tree or not
seed: int,
the random seed to use
draw: bool,
whether to draw the graph or not
Returns:
-------
graph: networkx Digraph"""
# if we want to generate a directed graph, we generate two undirected graphs
# of the same size and assemble them in one single directed graph by saying the
# vertices of the first are in the direction left -> right and the inverse for the second
# Compute the number of edges corresponding to the given density
n_edges = int(density * n_nodes * (n_nodes - 1) / 2)
# Create the graph
seed_1 = None if seed is None else seed + 1
if is_tree:
graph_0 = nx.random_tree(n_nodes, seed=seed)
if directed:
graph_1 = nx.random_tree(n_nodes, seed=seed_1)
else:
graph_1 = graph_0
else:
graph_0 = nx.gnm_random_graph(n_nodes, n_edges, seed)
if directed:
graph_1 = nx.gnm_random_graph(n_nodes, n_edges, seed_1)
else:
graph_1 = graph_0
graph_2 = nx.DiGraph()
graph_2.add_nodes_from(graph_0.nodes())
graph_2.add_edges_from([(u, v) for (u, v) in graph_0.edges()])
graph_2.add_edges_from([(v, u) for (u, v) in graph_1.edges()])
if draw:
plot_graph(graph_2, color_type="fabulous")
return graph_2
def genTree(G, cliquel):
"""Generates a graph composed of a random tree in wich each leaf is one of
the cliques in G."""
k = len(cliquel) #Number of cliques
if k < 2:
print("there must be more than 1 clique!")
#To determine the constant "3.8" it was tested the torso_nodes/nodes ratio for
#the function random tree, and it was discovered to be aprox 0.625, with a
#max value of 0.76 at low number of nodes, so to be sure, I used 0.8:
tree = nx.random_tree(int(k * 3.8))
#list of nodes with degree = 1:
leaves = [n for n, v in tree.nodes(data=True) if tree.degree()[n] == 1]
#The other nodes:
not_leaves = [n for n, v in tree.nodes(data=True) if tree.degree()[n] != 1]
#Since the tree must have the same amount of leaves as cliques, we make sure that happens:
cnt = 0
while len(leaves) != k:
#Because of the flies, we put a limit to the search of the tree:
if cnt == 1000:
print(
"surpassed 1000 tries and can't find random tree with #leaves>=#cliques"
)
1 / 0
cnt += 1
#if we obtain a tree with more leaves, we cut them:
if len(leaves) > k:
tree.remove_node(leaves.pop(random.randint(0, len(leaves) - 1)))
#otherwise, we try with other tree:
else:
tree = nx.random_tree(int(k * 3.8))
leaves = [
n for n, v in tree.nodes(data=True) if tree.degree()[n] == 1
]
not_leaves = [
n for n, v in tree.nodes(data=True) if tree.degree()[n] != 1
]
tree = clean_waste(tree)
#First, we make sure node ids from tree aren't repeated in G by making their
#numbers start when the nodes on G end:
tree = nx.convert_node_labels_to_integers(tree, len(G))
leaves = [n for n, v in tree.nodes(data=True) if tree.degree()[n] == 1]
not_leaves = [n for n, v in tree.nodes(data=True) if tree.degree()[n] != 1]
#Make leaves have the same name id as one node from each clique in G:
leaf_name_dic = dict(zip(leaves, cliquel))
tree = nx.relabel_nodes(tree, leaf_name_dic)
#Make the not-leaves have a new name so as to continue in order with the rest of nodes:
not_leaf_names = [len(G) + x for x in range(len(not_leaves))]
not_leaf_name_dic = dict(zip(not_leaves, not_leaf_names))
tree = nx.relabel_nodes(tree, not_leaf_name_dic)
#Combine The tree with G:
G = nx.compose(G, tree)
return G
def get_random_connected(nodes, nr_edges):
"""
Constructs a dictionary describing a random connected graph with a specified number of edges,
with the name of the vertices are taken from the 'nodes'
:param nodes: list of str
Name of the nodes to be used
:param nr_edges: int
The number of edges that the graph should have.
:return: dct
keys are the names of the nodes and values their neighbors
"""
nn = len(nodes)
min_edges = nn - 1
max_edges = nn * (nn - 1) / 2
if (nr_edges < min_edges) or (nr_edges > max_edges):
raise ValueError("Number of edges cannot be less than #vertices-1 or greater then #vertices * (#vertices-1)/2")
G = nx.random_tree(nn)
non_edges = list(nx.non_edges(G))
for _ in range(min_edges, nr_edges):
random_edge = random.choice(non_edges)
G.add_edge(random_edge[0], random_edge[1])
non_edges.remove(random_edge)
# Construct mapping to relabel nodes
mapping = {i: nodes[i] for i in range(len(nodes))}
nx.relabel_nodes(G=G, mapping=mapping, copy=False)
# Get the dictionary from the graph
adjacency_dct = nx.to_dict_of_lists(G)
return adjacency_dct
def testOriginaltoCluster(n, c, k):
G_test = nx.random_tree(n)
setAllNodeAttributes(G_test)
G_cluster = buildClusteredSet(G_test, c) #return cluster graph
#start tree decomposition
tree_decomp = approx.treewidth_min_degree(G_cluster)
print("cluster dict:", clusterDict)
print("rej node dict", rejectingNodeDict)
clearVisitedNodesAndDictionaries(G_cluster)
makeMatrix(G_cluster, G_cluster.number_of_nodes())
color_map = []
for nodeID in G_test.nodes():
if G_test.nodes[nodeID]['criticality'] >= c:
color_map.append('red')
else:
color_map.append('green')
fig2 = plt.figure(1)
G_tree = tree_decomp[1]
print(
"List of nodes, where each node is a bag, and each bag contains a set of nodes in the bag:\n",
list(G_tree.nodes()), "\nList of edges, where each edge is listed:\n",
list(G_tree.edges()))
nx.draw_networkx(G_tree,
pos=nx.spring_layout(G_tree, iterations=200),
arrows=False,
with_labels=True)
for i in G_tree.nodes():
print(list(i))
#nx.draw_networkx(G_cluster, node_color = color_map, pos=nx.spring_layout(G_test, iterations=1000), arrows=False, with_labels=True)
return G_cluster
def get_graph(num_nodes, k, criticality):
G_cluster = False
G = False
cluster_graphs, original_graphs = sgc.make_graphs(criticality, num_nodes)
graph_types = [
"ba-no-cycle", "ba-cycle", "er-no-cycle", "er-cycle", "ws-no-cycle",
"ws-cycle"
]
while G_cluster == False:
G = nx.random_tree(num_nodes)
G_cluster = cc.testOriginaltoCluster(G, num_nodes, criticality, True,
True)
cluster_graphs.append(G_cluster)
store_info(G_cluster, k)
graph_types.append("cluster no cycle")
G_cluster_cycle = False
while G_cluster_cycle == False:
G_cluster_cycle = cc.testOriginaltoCluster(G, num_nodes, criticality,
False, False)
cluster_graphs.append(G_cluster_cycle)
original_graphs.append(["tree", G])
graph_types.append("cluster cycle")
for original in original_graphs:
cc.showOriginalGraph(original[1], criticality)
plt.savefig(FILE_DIRECTORY_PREFIX + "saved-graphs/" + original[0] +
".png")
# plt.show()
return cluster_graphs, graph_types
"""
def create_rnd_trees(size, number, filename, dst_path, labeled=False, seed=1):
random.seed(seed)
for i in range(number):
G = nx.random_tree(size, seed + i)
GSnap = snap.TUNGraph()
if labeled:
labels = snap.TIntStrH()
for node in G.nodes(data=True):
id = node[0]
if labeled:
node_label = node[1]['predicate']
labels[int(id)] = str(node_label)
GSnap.AddNode(int(id))
for edge in G.edges():
GSnap.AddEdge(int(edge[0]), int(edge[1]))
FOut = snap.TFOut(dst_path + filename + "_" +
str(i).zfill(math.ceil(math.log10(number + 1))) +
".graph")
GSnap.Save(FOut)
FOut.Flush()
if labeled:
FOut = snap.TFOut(dst_path + filename + "_" +
str(i).zfill(math.ceil(math.log10(number + 1))) +
".labels")
labels.Save(FOut)
FOut.Flush()
def create_connected_graph(N, E):
G = nx.random_tree(N)
if nx.is_connected(G) == False:
raise Exception('Not a spanning tree!')
for (i, j) in G.edges: #Adds data to spanning tree portion of graph
p = random.random()
q = 0.5 * p
G.edges[i, j]['length'] = -np.log(p)
G.edges[i, j]['interdicted_length'] = -np.log(q) + np.log(p)
G_comp = nx.complete_graph(N)
while G.number_of_edges() < 0.5 * E: #generates remaining edges with data
edge = random.sample(list(set(G_comp.edges) - set(G.edges)), 1)
for (i, j) in edge:
p = random.random()
q = 0.5 * p
G.add_edge(i,
j,
length=-np.log(p),
interdicted_length=-np.log(q) + np.log(p))
G = G.to_directed()
if nx.is_strongly_connected(G) == False:
raise Exception('Directed graph is not strongly connected')
nx.draw(G, with_labels=True)
plt.show()
plt.savefig("path.png")
return G
def random(cls, numVertices: int):
'''Return a random tree of given size'''
if numVertices <= 0:
return nx.Graph()
graph = nx.random_tree(int(numVertices))
return cls(graph, 0)
def generate_test ( filenum, isCyclic, nodes, edges, prefix=None ):
while True:
if isCyclic:
G = nx.gnm_random_graph(nodes, edges)
else:
G = nx.random_tree(nodes)
if nx.is_connected(G): # ensure connected graph
break
# nx.draw(G, with_labels=True, font_weight='bold')
# plt.savefig("{}tests/test{}.png".format(prefix if prefix else "",filenum))
# plt.close()
with open("{}tests/test{}.txt".format(prefix if prefix else "",filenum), "w") as infile:
infile.write("{}\n".format(nodes))
A = nx.adjacency_matrix(G).toarray()
for row in A:
for col in row:
infile.write("{} ".format(col))
infile.write("\n")
with open("{}queries/query{}.txt".format(prefix if prefix else "",filenum), "w") as qfile:
source = random.randrange(nodes)
qfile.write("{}\n".format(source))
target = source
while target == source:
target = random.randrange(nodes) # make sure source and target are different nodes
qfile.write("{}\n".format(target))
with open("{}edgelists/edgelist{}.txt".format(prefix if prefix else "",filenum), "wb") as efile:
nx.write_edgelist(G, efile, data=False)
def generate_random_uniform(N, T, G_method, seed=1234):
rng = np.random.RandomState(seed)
N_ = 4 if N >= 5 else N - 1
switcher = {
'complete': nx.complete_graph(N),
'path': nx.path_graph(N),
'cycle': nx.cycle_graph(N),
'regular': nx.random_regular_graph(N_, N, seed=rng),
'wheel': nx.wheel_graph(N),
'tree': nx.random_tree(N, seed=rng),
'chordal': nx.Graph(nx.chordal_cycle_graph(N)),
}
G = switcher.get(G_method)
player_list = []
for n in range(N):
p = Player(x=rng.uniform(3, -3, T),
sm=13.5,
s0=0,
ram=5,
ec=0.9,
ed=0.9)
player_list.append(p)
buying_price = np.ones(T) * 3.0
selling_price = np.ones(T) * 1.0
game = Game(player_list, buying_price, selling_price, G)
game.graphtype = G_method
game.seed = seed
return game
def test_from_nx_graph():
for _ in range(10):
nx_graph = nx.random_tree(10)
g = Graph()
g.from_nx_graph(nx_graph=nx_graph)
assert compare_lists_unordered(g.vertices, list(nx_graph.nodes))
assert compare_lists_unordered(g.edges, list(set(nx_graph.edges).union({(edge[1], edge[0]) for edge in nx_graph.edges})))
def generate_test(filenum, isTree, nodes, edges, prefix=None):
if isTree:
G = nx.random_tree(nodes)
else:
G = nx.gnm_random_graph(nodes, edges)
# nx.draw(G, with_labels=True, font_weight='bold')
# plt.savefig("{}tests/test{}.png".format(prefix if prefix else "",filenum))
# plt.close()
with open("{}tests/test{}.txt".format(prefix if prefix else "", filenum),
"w") as infile:
infile.write("{}\n".format(nodes))
A = nx.adjacency_matrix(G).toarray()
for row in A:
for col in row:
infile.write("{} ".format(col))
infile.write("\n")
with open(
"{}answers/answer{}.txt".format(prefix if prefix else "", filenum),
"w") as outfile:
try:
cycle = nx.find_cycle(G)
except nx.NetworkXNoCycle:
cycle = None
outfile.write("no" if cycle else "yes")
def generate_graph(size, graph_type):
if graph_type == 'random':
G = nx.dense_gnm_random_graph(size, size * 5, seed=SEED)
elif graph_type == 'small_world':
G = nx.watts_strogatz_graph(size, 8, 0.25, seed=SEED)
elif graph_type == 'small_world_sparse':
G = nx.watts_strogatz_graph(size, size / 8, 0.25, seed=SEED)
elif graph_type == 'scale_free':
# regular expts
G = nx.barabasi_albert_graph(size, 8, seed=SEED)
# implementation, celer expts - 10 node graph
# G = nx.barabasi_albert_graph(size, 5, seed=12)
elif graph_type == 'scale_free_sparse':
G = nx.barabasi_albert_graph(size, size / 8, seed=SEED)
elif graph_type == 'tree':
G = nx.random_tree(size, seed=SEED)
# remove self loops and parallel edges
G.remove_edges_from(G.selfloop_edges())
G = nx.Graph(G)
print('Generated a ', graph_type, ' graph')
print('number of nodes: ', G.number_of_nodes())
print('Number of Edges: ', G.number_of_edges())
print('Number of connected components: ',
nx.number_connected_components(G))
return G
def testOriginaltoCluster(n, c, k):
G_test = nx.random_tree(n)
setAllNodeAttributes(G_test)
G_cluster = buildClusteredSet(G_test, c)
f = open("make_matrix.txt", "a")
f.write("cluster dictionary:" + str(clusterDict) + "\n")
f.write("rej node dictionary: " + str(rejectingNodeDict) + "\n")
f.write("edge data:" + str(G_cluster.edges.data()) + "\n")
f.write("node data:" + str(G_cluster.nodes.data()) + "\n")
f.close()
test1 = DP(G_cluster, G_cluster.number_of_nodes(), k)
maxval = DP_Improved(G_cluster, k)
print("payoff test DP is: ", test1)
print("payoff subtree DP is:", maxval)
clearVisitedNodesAndDictionaries(G_cluster)
makeMatrix(G_cluster, G_cluster.number_of_nodes())
color_map = []
for nodeID in G_test.nodes():
if G_test.nodes[nodeID]['criticality'] >= c:
color_map.append('red')
else:
color_map.append('green')
fig2 = plt.figure(1)
nx.draw_networkx(G_test,
node_color=color_map,
pos=nx.spring_layout(G_test, iterations=1000),
arrows=False,
with_labels=True)
return G_cluster
def blowUpIslands(n, p):
G = nx.random_tree(n)
for i in range(0, n):
if rand.random() < p:
G.remove_node(i)
return nx.number_connected_components(G)
def generate_struct_mask(struct, n_nodes, shuffle_nodes):
# a horrible collection of ifs due to args in nx constructors
if struct == "star":
g = nx.star_graph(n_nodes)
elif struct == "random_tree":
g = nx.random_tree(n_nodes)
elif struct == "powerlaw_tree":
g = nx.powerlaw_tree(n_nodes, gamma=3, seed=None)
elif struct == "binary_tree":
raise NotImplementedError("Implement a binary tree.")
elif struct == "path":
g = nx.path_graph(n_nodes)
elif struct == "cycle":
g = nx.cycle_graph(n_nodes)
elif struct == "ladder":
g = nx.ladder_graph(n_nodes)
elif struct == "grid":
m = np.random.choice(range(1, n_nodes+1))
n = n_nodes // m
g = nx.grid_2d_graph(m, n)
elif struct == "circ_ladder":
g = nx.circular_ladder_graph(n_nodes)
elif struct == "barbell":
assert n_nodes >= 4
m = np.random.choice(range(2, n_nodes-1))
blocks = (m, n_nodes-m)
g = nx.barbell_graph(*blocks)
elif struct == "loll":
assert n_nodes >= 2
m = np.random.choice(range(2, n_nodes+1))
g = nx.lollipop_graph(m, n_nodes-m)
elif struct == "wheel":
g = nx.wheel_graph(n_nodes)
elif struct == "bipart":
m = np.random.choice(range(n_nodes))
blocks = (m, n_nodes-m)
g = nx.complete_multipartite_graph(*blocks)
elif struct == "tripart":
# allowed to be zero
m, M = np.random.choice(range(n_nodes), size=2)
if m > M:
m, M = M, m
blocks = (m, M-m, n_nodes-M)
g = nx.complete_multipartite_graph(*blocks)
elif struct == "fc":
g = nx.complete_graph(n_nodes)
else:
raise NotImplementedError("Structure {} not implemented yet.".format(struct))
node_order = list(range(n_nodes))
if shuffle_nodes:
np.random.shuffle(node_order)
# a weird subclass by default; raises a deprecation warning
# with a new update of networkx, this should be updated to
# nx.convert_matrix.to_numpy_array
np_arr_g = nx.to_numpy_matrix(g, nodelist=node_order)
return np_arr_g.astype(int)
def createClusterGraph(n):
G = nx.random_tree(n)
for i in G.nodes():
rand = random.randint(1, 15)
G.nodes[i]['weight'] = rand
for neighbor in nx.neighbors(G, i):
rand2 = random.randint(0, rand)
G.add_edge(i, neighbor, weight=rand2)
return G
def create_graph(number_of_nodes):
# Create a random tree with x nodes
global G
G = nx.random_tree(number_of_nodes, seed=seed)
pos = nx.nx_pydot.graphviz_layout(G, prog='dot', root=0)
# Draw the graph
nx.draw(G, pos, with_labels=True)
plt.show()
return G
def directed_random_tree(n, arrows_from_root, seed):
G = nx.random_tree(n, seed)
betweeness = nx.betweenness_centrality(G, normalized=False, seed=0)
root = max(betweeness, key=lambda key: betweeness[key])
T = nx.bfs_tree(G, root) # Arrows point away from root
if arrows_from_root:
return T
else:
return nx.DiGraph(nx.reverse(T, copy=False)) # Cast from ReverseView
def random_ordered_tree(n, seed=None, pool=None):
import kwarray
rng = kwarray.ensure_rng(seed, 'python')
tree = nx.dfs_tree(nx.random_tree(n, seed=seed))
otree = nx.OrderedDiGraph()
otree.add_edges_from(tree.edges)
if pool is not None:
for node in otree.nodes:
otree.nodes[node]['label'] = rng.choice(pool)
return otree
def make_tree(request):
"""Function for making a tree
This function is getting a graph,
and returns a tree or "0".
"""
raw_data = request.GET.dict()
graph_data = json.loads(raw_data["graph"])
graph = nx.random_tree(len(graph_data["nodes"]))
data = cn.to_json(nx.to_numpy_matrix(graph).tolist(), graph_data)
return JsonResponse(data)
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 random_rooted_tree(n: int, mine=True) -> DiGraph:
# Node 0 is the root
if mine:
# Tends to produce a wider, shorter tree
di_g = my_random_rooted_tree(n)
else:
# Tends to produce a taller, skinnier tree
# Graph starts out with all bidirectional edges
di_g = nx.random_tree(n).to_directed()
# Remove edges pointing towards the root
di_g = to_directed_tree(di_g)
return di_g
def test_tree(self):
for i in range(10):
N = np.random.randint(2, 50)
G = nx.random_tree(N)
mapping = {
i: j
for i, j in zip(range(N), np.random.permutation(range(N)))
}
H = nx.relabel_nodes(G, mapping)
assert nx.is_isomorphic(G, H)
assert is_possibly_isomorphic(G, H, N)
def create_graph(topology, info):
if topology == 'simple':
return nx.barabasi_albert_graph(info['num_nodes'], info['avg_degree'])
elif topology == 'star':
return nx.star_graph(info['num_nodes'])
elif topology == 'tree':
return nx.random_tree(info['num_nodes'])
elif topology == 'ladder':
return nx.ladder_graph(round(info['num_nodes'] / 2))
else:
print("Invalid network style received. Aborting...")
exit(1)
def get_graph_by_type(graph_type: str, num_nodes: int, **kwargs) -> nx.Graph:
if graph_type == "E-R":
return nx.erdos_renyi_graph(n=num_nodes, **kwargs)
elif graph_type == "Random Tree":
return nx.random_tree(n=num_nodes, **kwargs)
elif graph_type == "r-ary":
return nx.full_rary_tree(n=num_nodes, **kwargs)
elif graph_type == "Planted Partition":
return nx.planted_partition_graph(**kwargs)
elif graph_type == "Line":
return nx.path_graph(n=num_nodes, **kwargs)
elif graph_type == "Barabási–Albert":
return nx.barabasi_albert_graph(n=num_nodes, **kwargs)
def tree_insertion(num_nodes, num_edges, return_tree=False):
tree = nx.random_tree(num_nodes)
chordal = Graph(tree)
while len(chordal.edges) < num_edges:
u, v = random.sample(chordal.nodes, 2)
chordal.add_edge(u, v)
while not nx.is_chordal(chordal):
chordal.remove_edge(u, v)
u, v = random.sample(chordal.nodes, 2)
chordal.add_edge(u, v)
if not return_tree:
return chordal
return tree, chordal
def test_random_forest_compare_with_tree_dp():
# Generate tree on 50 edges, then leave only 40 random edges.
gr_size, al_size = 50, 5
edges = list(networkx.random_tree(gr_size).edges())
random.shuffle(edges)
edges = edges[0:40]
model = PairWiseFiniteModel(gr_size, 5)
model.set_field(np.random.random((gr_size, al_size)))
for v1, v2 in edges:
model.add_interaction(v1, v2, np.random.random((al_size, al_size)))
assert_results_close(model.infer(algorithm='message_passing'),
model.infer(algorithm='tree_dp'))
def test_trees(self):
"""The barycenter of a tree is a single vertex or an edge.
See [West01]_, p. 78.
"""
prng = Random(0xdeadbeef)
for i in range(50):
RT = nx.random_tree(prng.randint(1, 75), prng)
b = self.barycenter_as_subgraph(RT)
if len(b) == 2:
assert_equal(b.size(), 1)
else:
assert_equal(len(b), 1)
assert_equal(b.size(), 0)
def test_random_tree():
"""Tests that a random tree is in fact a tree."""
T = nx.random_tree(10, seed=1234)
assert_true(nx.is_tree(T))