[PYTHON] 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.

Example

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

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).

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()

Example 2 (when m2 = 0)

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

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 $.

Example

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

complete_graph

complete_graph(n, create_using=None)

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

Example 1 (when n is an integer type)

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

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_multipartite_graph

complete_multipartite_graph(*subset_sizes)

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()

circular_ladder_graph

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

Example

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

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`.

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.

cycle_graph

cycle_graph(n, create_using=None)

Example

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

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

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

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.

Example

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

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.

Example

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

ladder_graph

ladder_graph(n, create_using=None)

Returns a ladder graph.

Example

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

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).

Example

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

null_graph

null_graph(create_using=None)

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

Example

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

path_graph

path_graph(n, create_using=None)

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

G=nx.path_graph(5)
plt.cla()
nx.draw_networkx(G)
plt.show()

star_graph

star_graph(n, create_using=None)

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

G=nx.star_graph(5)
plt.cla()
nx.draw_networkx(G)
plt.show()

trivial_graph

trivial_graph(create_using=None)

Returns the simplest graph consisting of only one node.

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

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).

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

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.

Example

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

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.

G=nx.margulis_gabber_galil_graph(3)
pos=nx.circular_layout(G)
plt.cla()
nx.draw_networkx(G)
plt.show()

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.

G=nx.chordal_cycle_graph(7)
pos=nx.circular_layout(G)
plt.cla()
nx.draw_networkx(G,pos)
plt.show()

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()

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.

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

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.

reference

• https://networkx.org/documentation/networkx-2.4/reference/generators.html