#!/usr/bin/env python3
# -*- coding: utf-8 -*-
#
# This file classic.py is referred and derived from project NetworkX,
#
# https://github.com/networkx/networkx/blob/master/networkx/generators/classic.py
#
# which has the following license:
#
# Copyright (C) 2004-2020, NetworkX Developers
# Aric Hagberg <[email protected]>
# Dan Schult <[email protected]>
# Pieter Swart <[email protected]>
# All rights reserved.
#
# This file is part of NetworkX.
#
# NetworkX is distributed under a BSD license; see LICENSE.txt for more
# information.
#
import itertools
from itertools import accumulate
import networkx as nxa
from networkx.utils import nodes_or_number
from networkx.utils import pairwise
from graphscope import nx
from graphscope.nx import NetworkXError
from graphscope.nx.classes.graph import Graph
from graphscope.nx.utils.compat import patch_docstring
__all__ = [
"balanced_tree",
"barbell_graph",
"binomial_tree",
"complete_graph",
"complete_multipartite_graph",
"circular_ladder_graph",
"circulant_graph",
"cycle_graph",
"dorogovtsev_goltsev_mendes_graph",
"empty_graph",
"full_rary_tree",
"ladder_graph",
"lollipop_graph",
"null_graph",
"path_graph",
"star_graph",
"trivial_graph",
"turan_graph",
"wheel_graph",
]
# -------------------------------------------------------------------
# Some Classic Graphs
# -------------------------------------------------------------------
def _tree_edges(n, r):
if n == 0:
return
# helper function for trees
# yields edges in rooted tree at 0 with n nodes and branching ratio r
nodes = iter(range(n))
parents = [next(nodes)] # stack of max length r
while parents:
source = parents.pop(0)
for i in range(r):
try:
target = next(nodes)
parents.append(target)
yield source, target
except StopIteration:
break
[docs]@patch_docstring(nxa.full_rary_tree)
def full_rary_tree(r, n, create_using=None):
G = empty_graph(n, create_using)
G.add_edges_from(_tree_edges(n, r))
return G
[docs]@patch_docstring(nxa.balanced_tree)
def balanced_tree(r, h, create_using=None):
# The number of nodes in the balanced tree is `1 + r + ... + r^h`,
# which is computed by using the closed-form formula for a geometric
# sum with ratio `r`. In the special case that `r` is 1, the number
# of nodes is simply `h + 1` (since the tree is actually a path
# graph).
if r == 1:
n = h + 1
else:
# This must be an integer if both `r` and `h` are integers. If
# they are not, we force integer division anyway.
n = (1 - r ** (h + 1)) // (1 - r)
return full_rary_tree(r, n, create_using=create_using)
[docs]@patch_docstring(nxa.barbell_graph)
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
[docs]@patch_docstring(nxa.binomial_tree)
def binomial_tree(n, create_using=None):
G = nx.empty_graph(1, create_using)
N = 1
for i in range(n):
# Use G.edges() to ensure 2-tuples. G.edges is 3-tuple for MultiGraph
edges = [(u + N, v + N) for (u, v) in G.edges()]
G.add_edges_from(edges)
G.add_edge(0, N)
N *= 2
return G
[docs]@nodes_or_number(0)
@patch_docstring(nxa.complete_graph)
def complete_graph(n, create_using=None):
n_name, nodes = n
G = empty_graph(n_name, create_using)
if len(nodes) > 1:
if G.is_directed():
edges = itertools.permutations(nodes, 2)
else:
edges = itertools.combinations(nodes, 2)
G.add_edges_from(edges)
return G
[docs]@patch_docstring(nxa.circular_ladder_graph)
def circular_ladder_graph(n, create_using=None):
G = ladder_graph(n, create_using)
G.add_edge(0, n - 1)
G.add_edge(n, 2 * n - 1)
return G
[docs]@patch_docstring(nxa.circulant_graph)
def circulant_graph(n, offsets, create_using=None):
G = empty_graph(n, create_using)
for i in range(n):
for j in offsets:
G.add_edge(i, (i - j) % n)
G.add_edge(i, (i + j) % n)
return G
[docs]@nodes_or_number(0)
@patch_docstring(nxa.cycle_graph)
def cycle_graph(n, create_using=None):
n_orig, nodes = n
G = empty_graph(nodes, create_using)
G.add_edges_from(pairwise(nodes))
G.add_edge(nodes[-1], nodes[0])
return G
[docs]@patch_docstring(nxa.dorogovtsev_goltsev_mendes_graph)
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
[docs]@nodes_or_number(0)
def empty_graph(n=0, create_using=None, default=nx.Graph, **kw):
"""Returns the empty graph with n nodes and zero edges.
Parameters
----------
n : int or iterable container of nodes (default = 0)
If n is an integer, nodes are from `range(n)`.
If n is a container of nodes, those nodes appear in the graph.
create_using : Graph Instance, Constructor or None
Indicator of type of graph to return.
If a Graph-type instance, then clear and use it.
If None, use the `default` constructor.
If a constructor, call it to create an empty graph.
default : Graph constructor (optional, default = nx.Graph)
The constructor to use if create_using is None.
If None, then nx.Graph is used.
This is used when passing an unknown `create_using` value
through your home-grown function to `empty_graph` and
you want a default constructor other than nx.Graph.
Examples
--------
>>> G = nx.empty_graph(10)
>>> G.number_of_nodes()
10
>>> G.number_of_edges()
0
>>> G = nx.empty_graph("ABC")
>>> G.number_of_nodes()
3
>>> sorted(G)
['A', 'B', 'C']
"""
if create_using is None:
G = default(**kw)
elif hasattr(create_using, "_adj"):
# create_using is a NetworkX style Graph
create_using.clear()
G = create_using
else:
# try create_using as constructor
G = create_using(**kw)
n_name, nodes = n
G.add_nodes_from(nodes)
return G
[docs]@patch_docstring(nxa.ladder_graph)
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
[docs]@nodes_or_number([0, 1])
@patch_docstring(nxa.lollipop_graph)
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
[docs]@patch_docstring(nxa.null_graph)
def null_graph(create_using=None):
G = empty_graph(0, create_using)
return G
[docs]@nodes_or_number(0)
@patch_docstring(nxa.path_graph)
def path_graph(n, create_using=None):
n_name, nodes = n
G = empty_graph(nodes, create_using)
G.add_edges_from(pairwise(nodes))
return G
[docs]@nodes_or_number(0)
@patch_docstring(nxa.star_graph)
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
[docs]def trivial_graph(create_using=None):
"""Return the Trivial graph with one node (with label 0) and no edges."""
G = empty_graph(1, create_using)
return G
[docs]@patch_docstring(nxa.turan_graph)
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
[docs]@nodes_or_number(0)
@patch_docstring(nxa.wheel_graph)
def wheel_graph(n, create_using=None):
n_name, nodes = n
if n_name == 0:
G = empty_graph(0, create_using)
return G
G = star_graph(nodes, create_using)
if len(G) > 2:
G.add_edges_from(pairwise(nodes[1:]))
G.add_edge(nodes[-1], nodes[1])
return G
[docs]@patch_docstring(nxa.complete_multipartite_graph)
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