def make_small_graph(graph_description, create_using=None):
if graph_description[0] not in ("adjacencylist", "edgelist"):
raise NetworkXError("ltype must be either adjacencylist or edgelist")
ltype = graph_description[0]
name = graph_description[1]
n = graph_description[2]
G = empty_graph(n, create_using)
nodes = G.nodes()
if ltype == "adjacencylist":
adjlist = graph_description[3]
if len(adjlist) != n:
raise NetworkXError("invalid graph_description")
G.add_edges_from([(u - 1, v) for v in nodes for u in adjlist[v]])
elif ltype == "edgelist":
edgelist = graph_description[3]
for e in edgelist:
v1 = e[0] - 1
v2 = e[1] - 1
if v1 < 0 or v1 > n - 1 or v2 < 0 or v2 > n - 1:
raise NetworkXError("invalid graph_description")
G.add_edge(v1, v2)
G.name = name
return G
def turan_graph(n, r):
if not 1 <= r <= n:
raise NetworkXError("Must satisfy 1 <= r <= n")
partitions = [n // r] * (r - (n % r)) + [n // r + 1] * (n % r)
G = complete_multipartite_graph(*partitions)
return G
def complete_multipartite_graph(*subset_sizes):
# The complete multipartite graph is an undirected simple graph.
G = Graph()
if len(subset_sizes) == 0:
return G
# set up subsets of nodes
try:
extents = pairwise(accumulate((0, ) + subset_sizes))
subsets = [range(start, end) for start, end in extents]
except TypeError:
subsets = subset_sizes
# add nodes with subset attribute
# while checking that ints are not mixed with iterables
try:
for (i, subset) in enumerate(subsets):
G.add_nodes_from(subset, subset=i)
except TypeError:
raise NetworkXError("Arguments must be all ints or all iterables")
# Across subsets, all vertices should be adjacent.
# We can use itertools.combinations() because undirected.
for subset1, subset2 in itertools.combinations(subsets, 2):
G.add_edges_from(itertools.product(subset1, subset2))
return G
def ladder_graph(n, create_using=None):
G = empty_graph(2 * n, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
G.add_edges_from(pairwise(range(n)))
G.add_edges_from(pairwise(range(n, 2 * n)))
G.add_edges_from((v, v + n) for v in range(n))
return G
def make_small_undirected_graph(graph_description, create_using=None):
"""
Return a small undirected graph described by graph_description.
See make_small_graph.
"""
G = empty_graph(0, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
return make_small_graph(graph_description, G)
def star_graph(n, create_using=None):
n_name, nodes = n
if isinstance(n_name, int):
nodes = nodes + [n_name] # there should be n+1 nodes
first = nodes[0]
G = empty_graph(nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
G.add_edges_from((first, v) for v in nodes[1:])
return G
def dorogovtsev_goltsev_mendes_graph(n, create_using=None):
G = empty_graph(0, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
if G.is_multigraph():
raise NetworkXError("Multigraph not supported")
G.add_edge(0, 1)
if n == 0:
return G
new_node = 2 # next node to be added
for i in range(1, n + 1): # iterate over number of generations.
last_generation_edges = list(G.edges())
number_of_edges_in_last_generation = len(last_generation_edges)
for j in range(0, number_of_edges_in_last_generation):
G.add_edge(new_node, last_generation_edges[j][0])
G.add_edge(new_node, last_generation_edges[j][1])
new_node += 1
return G
def barbell_graph(m1, m2, create_using=None):
if m1 < 2:
raise NetworkXError("Invalid graph description, m1 should be >=2")
if m2 < 0:
raise NetworkXError("Invalid graph description, m2 should be >=0")
# left barbell
G = complete_graph(m1, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
# connecting path
G.add_nodes_from(range(m1, m1 + m2 - 1))
if m2 > 1:
G.add_edges_from(pairwise(range(m1, m1 + m2)))
# right barbell
G.add_edges_from((u, v) for u in range(m1 + m2, 2 * m1 + m2)
for v in range(u + 1, 2 * m1 + m2))
# connect it up
G.add_edge(m1 - 1, m1)
if m2 > 0:
G.add_edge(m1 + m2 - 1, m1 + m2)
return G
def lollipop_graph(m, n, create_using=None):
m, m_nodes = m
n, n_nodes = n
M = len(m_nodes)
N = len(n_nodes)
if isinstance(m, int):
n_nodes = [len(m_nodes) + i for i in n_nodes]
if M < 2:
raise NetworkXError("Invalid graph description, m should be >=2")
if N < 0:
raise NetworkXError("Invalid graph description, n should be >=0")
# the ball
G = complete_graph(m_nodes, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
# the stick
G.add_nodes_from(n_nodes)
if N > 1:
G.add_edges_from(pairwise(n_nodes))
# connect ball to stick
if M > 0 and N > 0:
G.add_edge(m_nodes[-1], n_nodes[0])
return G
def LCF_graph(n, shift_list, repeats, create_using=None):
if n <= 0:
return empty_graph(0, create_using)
# start with the n-cycle
G = cycle_graph(n, create_using)
if G.is_directed():
raise NetworkXError("Directed Graph not supported")
G.name = "LCF_graph"
nodes = sorted(list(G))
n_extra_edges = repeats * len(shift_list)
# edges are added n_extra_edges times
# (not all of these need be new)
if n_extra_edges < 1:
return G
for i in range(n_extra_edges):
shift = shift_list[i % len(shift_list)] # cycle through shift_list
v1 = nodes[i % n] # cycle repeatedly through nodes
v2 = nodes[(i + shift) % n]
G.add_edge(v1, v2)
return G
def predecessors(self, n):
try:
return iter(self._pred[n])
except KeyError:
raise NetworkXError("The node %s is not in the digraph." % (n, ))