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 successors(self, n):
"""Returns an iterator over successor nodes of n.
A successor of n is a node m such that there exists a directed
edge from n to m.
Parameters
----------
n : node
A node in the graph
Raises
-------
KeyError
If n is not in the graph.
See Also
--------
predecessors
Notes
-----
neighbors() and successors() are the same.
"""
try:
return iter(self._succ[n])
except KeyError:
raise NetworkXError("The node %s is not in the digraph." % (n, ))
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 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 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 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 predecessors(self, n):
"""Returns an iterator over predecessor nodes of n.
A predecessor of n is a node m such that there exists a directed
edge from m to n.
Parameters
----------
n : node
A node in the graph
Raises
-------
Error
If n is not in the graph.
See Also
--------
successors
"""
try:
return iter(self._pred[n])
except KeyError:
raise NetworkXError("The node %s is not in the digraph." % (n, ))