NetworkX graph generator list

A list of graphs that can be created with NetworkX.

Previous information

The version of NetworkX is 2.4. This is a Japanese translation of the Official Documentation. Not all are covered. Please let us know if the translation is incorrect.

Please import networkx and matplotlib.pyplot in advance to execute the code below.

import networkx as nx
import matplotlib.pyplot as plt

Classic (classical graph)

balanced tree

balanced_tree(r, h, create_using=None)

Returns a perfectly balanced r branch tree with a height of h.

Parameters Type Description
r int The number of branches of the tree. Each node has r child nodes.
h int Tree height
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

#balanced_tree
G=nx.balanced_tree(3,2)
plt.cla()
nx.draw_networkx(G)
plt.show()

balanced_tree.png

Barbell graph

barbell_graph(m1, m2, create_using=None)

Returns a barbell graph (a graph in which two complete graphs consisting of m1 nodes are connected by a single path consisting of m2 nodes).

Parameters Type Description
m1 int Left and right complete graph(bell)Number of. m1>1
m2 int The number of nodes on the route connecting the left and right complete graphs. m2>=0
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Node numbering method Complete graph on the left: 0,1, ..., m1-1 Route: m1, m1 + 1, ..., m1 + m2-1 Complete graph on the right: m1 + m2, m1 + m2 + 1, ..., 2 * m1 + m2-1

Example 1

#barbell_graph
G=nx.barbell_graph(5,2)
plt.cla()
nx.draw_networkx(G)
plt.show()

barbell_graph1.png

Example 2 (when m2 = 0)

G=nx.barbell_graph(5,0)
plt.cla()
nx.draw_networkx(G)
plt.show()

barbell_graph2.png

binomial_tree

binomial_tree(n)

Returns a binary tree of degree n. The number of nodes is $ 2 ^ n $ and the number of edges is $ 2 ^ n-1 $.

Parameters Type Description
n int Degree of tree

Example

G=nx.binomial_tree(3)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

complete_graph

complete_graph(n, create_using=None)

Returns a graph in which one node is bound to all other nodes.

Parameters Type Description
n int or iterable container of nodes When n is an integer type, the node is range(n)It is created from. When n is an iterable container for nodes, graphs are created with those nodes
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example 1 (when n is an integer type)

G=nx.complete_graph(6)
plt.cla()
nx.draw_networkx(G)
plt.show()

complete_graph1.png

Example 2 (when n is a container for nodes)

G=nx.complete_graph(range(12,18))
plt.cla()
nx.draw_networkx(G)
plt.show()

complete_graph2.png

complete_multipartite_graph

complete_multipartite_graph(*subset_sizes)

Parameters Type Description
subset_sizes taple of integers or tuple of node iterables When n is an integer, each subset of the multipartite graph has n vertices. When n is iterable, a graph will be created with those nodes
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example Create a complete multipartite graph consisting of three subsets, each with a few nodes.

G=nx.complete_multipartite_graph(2,3,3)
plt.cla()
nx.draw_networkx(G)
plt.show()

complete_multi_graph.png

circular_ladder_graph

circular_ladder_graph(n, create_using=None) Returns a circular ladder graph of length n.

Parameters Type Description
n int Length of one lap
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.circular_ladder_graph(10)
plt.cla()
nx.draw_networkx(G)
plt.show()

circular_ladder_graph.png

circulant_graph

circulant_graph(n, offsets, create_using=None)

Returns a circular graph consisting of n nodes. Which node a node connects to is specified by ʻoffsets`.

Parameters Type Description
n int Number of nodes
offsets lists of integers List of node offsets
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.circulant_graph(10,[1,2])
plt.cla()
nx.draw_networkx(G)
plt.show()

Since ʻoffsets = [1,2]`, the vertices i are connected to the vertices i + 1 and i + 2, respectively. Vertex 0 is connected to vertices 1 and 2, vertex 1 is connected to vertices 2 and 3, ..., and vertex 9 is connected to vertices 0 and 1.

circulant_graph.png

cycle_graph

cycle_graph(n, create_using=None)

Parameters Type Description
n int or iterble container of nodes When n is an integer type, the node is range(n)It is created from. When n is an iterable container for nodes, graphs are created with those nodes
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.cycle_graph(10)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

dorogovtsev_goltsev_mendes_graph (Dorogovstev-Goltsev-Mendes graph)

dorogovtsev_goltsev_mendes_graph(n, create_using=None)

Returns the graph created by the Dorogovstev-Goltsev-Mendes algorithm.

Original paper https://arxiv.org/abs/cond-mat/0112143

Parameters Type Description
n int Number of generations
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create
G=nx.dorogovtsev_goltsev_mendes_graph(3)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

empty_graph (empty graph with nodes)

empty_graph(n=0, create_using=None, default=<class 'networkx.classes.graph.Graph'>)

Returns a graph of n nodes with no edges.

Parameters Type Description
n int Number of nodes
create_using Graph Instance, Constructor or None The type of graph you want to create. When None is specifieddefaultUse the constructor.
default Graph constructor (optional, default = nx.Graph) create_using=NoneConstructor used when.

Example

G=nx.empty_graph(10)
plt.cla()
nx.draw_networkx(G,pos)
plt.show()

image.png

How to use create_using

The variable create_using must be a Graph constructor or a "graph" -like object.

There are three main uses for create_using.

  1. Specify the nature of the null graph.
  2. Make an existing graph a null graph
  3. When creating your own graph creation function, allow you to pass your favorite graph constructor to create_using.
Example of 1

Create an empty directed graph (DiGraph).

n = 10
G = nx.empty_graph(n, create_using=nx.DiGraph)
2 examples

Creates an empty graph G2 with edges removed from the complete graph G1.

n=5
G1=nx.complete_graph(n)
G1.number_of_edges() #10
G2=nx.empty_graph(n,create_using=G1)
G2.number_of_edges() #0
3 examples

For your own graph creation function mygraph, set to use the default constructor nx.MultiGraph if create_using is not specified, and to use the specified constructor otherwise.

def mygraph(n, create_using=None):
    G = nx.empty_graph(n, create_using, default=nx.MultiGraph)
    G.add_edges_from([(0, 1), (0, 1)])
    return G
G = mygraph(3)
G.is_multigraph() #True

G = mygraph(3, nx.Graph)
G.is_multigraph() #False

full_rary_tree (all r branches)

full_rary_tree(r, n, create_using=None)

Creates all r branches consisting of n nodes. Every node is a leaf or has r child nodes.

Parameters Type Description
r int Number of branches in the tree
n int Number of nodes
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.full_rary_tree(3,16)
pos=nx.spring_layout(G,iterations=1000)
plt.cla()
nx.draw_networkx(G,pos)
plt.show()

image.png

ladder_graph

ladder_graph(n, create_using=None)

Returns a ladder graph.

Parameters Type Description
n int Ladder length
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.ladder_graph(7)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

lollipop_graph

lollipop_graph(m, n, create_using=None)

Returns a lollipop graph (a complete graph of m nodes and a path of n nodes connected to it).

Parameters Type Description
m int or iterable container of nodes (default = 0) Number of nodes that make up a complete graph
n int or iterable container of nodes (default = 0)) Number of nodes that make up the route
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.lollipop_graph(6,3)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

null_graph

null_graph(create_using=None)

Returns a graph with no nodes or edges. See ʻempty_graph for how to use create_using`.

Parameters Type Description
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.null_graph()
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

path_graph

path_graph(n, create_using=None)

Returns a graph of n nodes that does not pass through the same node twice.

Parameters Type Description
n int or iterable Number of nodes
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create
G=nx.path_graph(5)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

star_graph

star_graph(n, create_using=None)

Returns a graph with n outer nodes concatenated for one central node.

Parameters Type Description
n int or iterable Number of outer peripheral nodes
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create
G=nx.star_graph(5)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

trivial_graph

trivial_graph(create_using=None)

Returns the simplest graph consisting of only one node.

Parameters Type Description
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create
G=nx.trivial_graph()
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

turan_graph

turan_graph(n, r)

Returns a complete multipartite graph with n nodes divided into r unconnected parts. The number of edges is the number rounded down to the fraction of n ** 2 * (r-1) / (2 * r).

Parameters Type Description
n int The number of nodes.
r int Number of unconnected parts. 1<=r<=Must be n.
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create
G=nx.turan_graph(6,3)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

The node is divided into three parts (0,1), (2,3), (4,5). Nodes that belong to the same part are not concatenated.

The graph given in the example says, "Three couples went to a cocktail party. At the venue, everyone shook hands with all the participants except themselves and their spouse. The relationship at that time was noded to the participants. , What kind of graph would you get if you express your handshake as an edge? ”Is the answer to the question. Therefore, it is called "Cocktail Party Graph".

wheel_graph

wheel_graph(n, create_using=None)

Returns a graph with n-1 perimeter nodes concatenated for a hub node.

Parameters Type Description
n int or iterable The number of nodes.
create_using NetworkX graph constructor, optional (default=nx.Graph) The type of graph you want to create

Example

G=nx.wheel_graph(10)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

Expander graph

It is a sparse graph with a strongly connected component.

margulis_gabber_galil_graph (Margulis-Gabber-Galil graph)

margulis_gabber_galil_graph(n, create_using=None)

Returns a Margulis-Gabber-Galil graph. It is an undirected multiplex graph with a node degree of 8. The second largest eigenvalue of the adjacency matrix in this graph is $ 5 \ sqrt {2} $. An error is returned if the graph is not directed or multiple graphs.

Parameters Type Description
n int or iterable Defines the number of nodes. The number of nodes isn^2is.
create_using NetworkX graph constructor, optional (default MultiGraph) The type of graph you want to create
G=nx.margulis_gabber_galil_graph(3)
pos=nx.circular_layout(G)
plt.cla()
nx.draw_networkx(G)
plt.show()

image.png

chordal_cycle_graph (cycle graph with strings)

chordal_cycle_graph(p, create_using=None)

Returns a cycle graph with chords (edges that are not part of the cycle but connect between two nodes on the cycle graph). Node x has a string for node y that satisfies x * y = 1 (mod p). An error is returned if the graph is not directed or multiple graphs.

Parameters Type Description
p prime number Defines the number of nodes. Must be a prime number.
create_using NetworkX graph constructor, optional (default MultiGraph) The type of graph you want to create
G=nx.chordal_cycle_graph(7)
pos=nx.circular_layout(G)
plt.cla()
nx.draw_networkx(G,pos)
plt.show()

image.png

Social Networks

The famous social network graph.

karate_club_graph (Zachary Karate Club)

karate_club_graph()

A network of members of the karate club surveyed by American social psychologist Zachary. You can see that it is divided into two factions centered on node 0 and nodes 32 and 33.

Zachary, Wayne W. “An Information Flow Model for Conflict and Fission in Small Groups.” Journal of Anthropological Research, 33, 452–473, (1977).

G=nx.karate_club_graph()
plt.figure(figsize=(8,6))
nx.draw_networkx(G)
plt.show()

image.png

davis_southern_women_graph (Davis et al. Southern Women Graph)

davis_southern_women_graph()

A network of 18 women in the southern United States surveyed by Davis et al. In the 1930s. This is a bipartite graph consisting of nodes representing 18 women and 14 participating events.

A. Davis, Gardner, B. B., Gardner, M. R., 1941. Deep South. University of Chicago Press, Chicago, IL.

image.png

florentine_families_graph (Florentine family)

florentine_families_graph()

It is the marriage relationship of influential families such as the Medici family in Renaissance Florence.

Ronald L. Breiger and Philippa E. Pattison Cumulated social roles: The duality of persons and their algebras,1 Social Networks, Volume 8, Issue 3, September 1986, Pages 215-256

image.png

les_miserables_graph()

les_miserables_graph()

It is a graph of the characters in the novel "Les Miserables".

D. E. Knuth, 1993. The Stanford GraphBase: a platform for combinatorial computing, pp. 74-87. New York: AcM Press.

image.png

reference

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