
    hn                     <   S r / SQrSSKJr  SSKrSSKJr  SSKJ	r	J
r
JrJr  S r\R                  " SSS	9S!S
 j5       r\\R                  " SSS	9S!S j5       5       r\\R                  " SSS	9S!S j5       5       r\\R                  " SSS	9S!S j5       5       r\R                  " SSS	9S!S j5       r\\R                  " SSS	9S!S j5       5       r\R                  " SSS	9S!S j5       r\R                  " SSS	9S!S j5       r\R                  " SSS	9S!S j5       r\R                  " SSS	9S 5       r\\R                  " SSS	9S!S j5       5       r\\R                  " SSS	9S!S j5       5       r\\R                  " SSS	9S!S j5       5       r\\R                  " SSS	9S!S j5       5       r\R                  " SSS	9S!S j5       r\\R                  " SSS	9S!S j5       5       r\R                  " SSS	9S 5       r\\R                  " SSS	9S!S j5       5       r \R                  " SSS	9S!S j5       r!\R                  " SSS	9S!S j5       r"\\R                  " SSS	9S!S j5       5       r#\R                  " SSS	9S!S j5       r$\\R                  " SSS	9S!S  j5       5       r%g)"zI
Various small and named graphs, together with some compact generators.

)	LCF_graph
bull_graphchvatal_graphcubical_graphdesargues_graphdiamond_graphdodecahedral_graphfrucht_graphheawood_graphhoffman_singleton_graphhouse_graphhouse_x_graphicosahedral_graphkrackhardt_kite_graphmoebius_kantor_graphoctahedral_graphpappus_graphpetersen_graphsedgewick_maze_graphtetrahedral_graphtruncated_cube_graphtruncated_tetrahedron_graphtutte_graph    wrapsN)NetworkXError)complete_graphcycle_graphempty_graph
path_graphc                 0   ^  [        T 5      U 4S j5       nU$ )z
A decorator which inspects the `create_using` argument and raises a
NetworkX exception when `create_using` is a DiGraph (class or instance) for
graph generators that do not support directed outputs.
c                     > UR                  S5      b7  [        R                  " US   S9nUR                  5       (       a  [	        S5      eT" U 0 UD6$ )Ncreate_usingr#   Directed Graph not supported)getnxr   is_directedr   )argskwargsGfuncs      K/var/www/html/env/lib/python3.13/site-packages/networkx/generators/small.pywrapper#_raise_on_directed.<locals>.wrapper3   sL    ::n%1F>,BCA}}#$BCCT$V$$    r   )r,   r.   s   ` r-   _raise_on_directedr1   ,   s"     4[% % Nr0   T)graphsreturns_graphc                 X   U S::  a  [        SU5      $ [        X5      nUR                  5       (       a  [        S5      eSUl        [        U5      nU[        U5      -  nUS:  a  U$ [        U5       H5  nX[        U5      -     nXWU -     n	XWU-   U -     n
UR                  X5        M7     U$ )aZ  
Return the cubic graph specified in LCF notation.

LCF (Lederberg-Coxeter-Fruchte) notation[1]_ is a compressed
notation used in the generation of various cubic Hamiltonian
graphs of high symmetry. See, for example, `dodecahedral_graph`,
`desargues_graph`, `heawood_graph` and `pappus_graph`.

Nodes are drawn from ``range(n)``. Each node ``n_i`` is connected with
node ``n_i + shift % n`` where ``shift`` is given by cycling through
the input `shift_list` `repeat` s times.

Parameters
----------
n : int
   The starting graph is the `n`-cycle with nodes ``0, ..., n-1``.
   The null graph is returned if `n` < 1.

shift_list : list
   A list of integer shifts mod `n`, ``[s1, s2, .., sk]``

repeats : int
   Integer specifying the number of times that shifts in `shift_list`
   are successively applied to each current node in the n-cycle
   to generate an edge between ``n_current`` and ``n_current + shift mod n``.

Returns
-------
G : Graph
   A graph instance created from the specified LCF notation.

Examples
--------
The utility graph $K_{3,3}$

>>> G = nx.LCF_graph(6, [3, -3], 3)
>>> G.edges()
EdgeView([(0, 1), (0, 5), (0, 3), (1, 2), (1, 4), (2, 3), (2, 5), (3, 4), (4, 5)])

The Heawood graph:

>>> G = nx.LCF_graph(14, [5, -5], 7)
>>> nx.is_isomorphic(G, nx.heawood_graph())
True

References
----------
.. [1] https://en.wikipedia.org/wiki/LCF_notation

r   r%   r      )	r   r   r(   r   namesortedlenrangeadd_edge)n
shift_listrepeatsr#   r+   nodesn_extra_edgesishiftv1v2s              r-   r   r   >   s    h 	Av1l++ 	A$A}}:;;AF1IEc*o-M q=!s:./q5\I?#	

2	 "
 Hr0   c                 Z    [         R                  " SS// SQ/ SQS/S/S.U S9nSUl        U$ )a>  
Returns the Bull Graph

The Bull Graph has 5 nodes and 5 edges. It is a planar undirected
graph in the form of a triangle with two disjoint pendant edges [1]_
The name comes from the triangle and pendant edges representing
respectively the body and legs of a bull.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    A bull graph with 5 nodes

References
----------
.. [1] https://en.wikipedia.org/wiki/Bull_graph.

r5      r   rE      )r   r5      r   r5   rE   rG   rH   r$   z
Bull Graphr'   from_dict_of_listsr6   r#   r+   s     r-   r   r      s;    4 	FyYA3A3?!	A AFHr0   c                 z    [         R                  " / SQ/ SQ/ SQ/ SQSS/SS/SS/SS/S/SS/S	.
U S
9nSUl        U$ )u  
Returns the Chvátal Graph

The Chvátal Graph is an undirected graph with 12 nodes and 24 edges [1]_.
It has 370 distinct (directed) Hamiltonian cycles, giving a unique generalized
LCF notation of order 4, two of order 6 , and 43 of order 1 [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    The Chvátal graph with 12 nodes and 24 edges

References
----------
.. [1] https://en.wikipedia.org/wiki/Chv%C3%A1tal_graph
.. [2] https://mathworld.wolfram.com/ChvatalGraph.html

)r5   rH      	   rE         )rG   rN      )rH   rR   rO   rQ   rS   
      
r   r5   rE   rG   rH   rQ   rN   rR   rS   rO   r$   zChvatal GraphrJ   rL   s     r-   r   r      s`    4 	1vBxBx2wtBx	
 "	A AFHr0   c                 p    [         R                  " / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQS	.U S
9nSUl        U$ )a  
Returns the 3-regular Platonic Cubical Graph

The skeleton of the cube (the nodes and edges) form a graph, with 8
nodes, and 12 edges. It is a special case of the hypercube graph.
It is one of 5 Platonic graphs, each a skeleton of its
Platonic solid [1]_.
Such graphs arise in parallel processing in computers.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    A cubical graph with 8 nodes and 12 edges

References
----------
.. [1] https://en.wikipedia.org/wiki/Cube#Cubical_graph

)r5   rG   rH   )r   rE   rR   r5   rG   rN   )r   rE   rQ   )r   rQ   rR   )rG   rH   rN   rP   )r5   rH   rN   )r   r5   rE   rG   rH   rQ   rN   rR   r$   zPlatonic Cubical GraphrJ   rL   s     r-   r   r      sD    6 			
 "	A &AFHr0   c                 4    [        S/ SQSU 5      nSUl        U$ )a[  
Returns the Desargues Graph

The Desargues Graph is a non-planar, distance-transitive cubic graph
with 20 nodes and 30 edges [1]_.
It is a symmetric graph. It can be represented in LCF notation
as [5,-5,9,-9]^5 [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Desargues Graph with 20 nodes and 30 edges

References
----------
.. [1] https://en.wikipedia.org/wiki/Desargues_graph
.. [2] https://mathworld.wolfram.com/DesarguesGraph.html
   )rQ   rO   irQ   zDesargues Graphr   r6   rL   s     r-   r   r   
  s     2 	"na6AAFHr0   c                 X    [         R                  " SS// SQ/ SQSS/S.U S9nSUl        U$ )a  
Returns the Diamond graph

The Diamond Graph is  planar undirected graph with 4 nodes and 5 edges.
It is also sometimes known as the double triangle graph or kite graph [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Diamond Graph with 4 nodes and 5 edges

References
----------
.. [1] https://mathworld.wolfram.com/DiamondGraph.html
r5   rE   rF   )r   r5   rG   )r   r5   rE   rG   r$   zDiamond GraphrJ   rL   s     r-   r   r   (  s8    . 	FyYAq6:	A AFHr0   c                 4    [        S/ SQSU 5      nSUl        U$ )a  
Returns the Platonic Dodecahedral graph.

The dodecahedral graph has 20 nodes and 30 edges. The skeleton of the
dodecahedron forms a graph. It is one of 5 Platonic graphs [1]_.
It can be described in LCF notation as:
``[10, 7, 4, -4, -7, 10, -4, 7, -7, 4]^2`` [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Dodecahedral Graph with 20 nodes and 30 edges

References
----------
.. [1] https://en.wikipedia.org/wiki/Regular_dodecahedron#Dodecahedral_graph
.. [2] https://mathworld.wolfram.com/DodecahedralGraph.html

rZ   )
rT   rR   rH   rT   r_   rR   r`   rH   rE   zDodecahedral Graphr\   rL   s     r-   r   r   F  s!    4 	":A|LA!AFHr0   c                     [        SU 5      nUR                  SS/SS/SS/SS/SS/S	S
/SS
/SS/SS/SS/S
S//5        SUl        U$ )ag  
Returns the Frucht Graph.

The Frucht Graph is the smallest cubical graph whose
automorphism group consists only of the identity element [1]_.
It has 12 nodes and 18 edges and no nontrivial symmetries.
It is planar and Hamiltonian [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Frucht Graph with 12 nodes and 18 edges

References
----------
.. [1] https://en.wikipedia.org/wiki/Frucht_graph
.. [2] https://mathworld.wolfram.com/FruchtGraph.html

rR   r   r5   rE   rS   rG   rO   rH   rQ   rT   rN   rU   zFrucht Graph)r   add_edges_fromr6   rL   s     r-   r	   r	   e  s~    4 	A|$AFFFFFGGGGFH	
  AFHr0   c                 4    [        SSS/SU 5      nSUl        U$ )a  
Returns the Heawood Graph, a (3,6) cage.

The Heawood Graph is an undirected graph with 14 nodes and 21 edges,
named after Percy John Heawood [1]_.
It is cubic symmetric, nonplanar, Hamiltonian, and can be represented
in LCF notation as ``[5,-5]^7`` [2]_.
It is the unique (3,6)-cage: the regular cubic graph of girth 6 with
minimal number of vertices [3]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Heawood Graph with 14 nodes and 21 edges

References
----------
.. [1] https://en.wikipedia.org/wiki/Heawood_graph
.. [2] https://mathworld.wolfram.com/HeawoodGraph.html
.. [3] https://www.win.tue.nl/~aeb/graphs/Heawood.html

   rQ   r[   rR   zHeawood Graphr\   rL   s     r-   r
   r
     s$    : 	"q"gq,/AAFHr0   c            
         [         R                  " 5       n [        S5       H  n[        S5       H  nU R                  SX4SXS-
  S-  45        U R                  SX4SXS-   S-  45        U R                  SX4SXS-
  S-  45        U R                  SX4SXS-   S-  45        [        S5       H"  nU R                  SX4SX1U-  U-   S-  45        M$     M     M     [         R                  " U 5      n SU l        U $ )us  
Returns the Hoffman-Singleton Graph.

The Hoffman–Singleton graph is a symmetrical undirected graph
with 50 nodes and 175 edges.
All indices lie in ``Z % 5``: that is, the integers mod 5 [1]_.
It is the only regular graph of vertex degree 7, diameter 2, and girth 5.
It is the unique (7,5)-cage graph and Moore graph, and contains many
copies of the Petersen graph [2]_.

Returns
-------
G : networkx Graph
    Hoffman–Singleton Graph with 50 nodes and 175 edges

Notes
-----
Constructed from pentagon and pentagram as follows: Take five pentagons $P_h$
and five pentagrams $Q_i$ . Join vertex $j$ of $P_h$ to vertex $h·i+j$ of $Q_i$ [3]_.

References
----------
.. [1] https://blogs.ams.org/visualinsight/2016/02/01/hoffman-singleton-graph/
.. [2] https://mathworld.wolfram.com/Hoffman-SingletonGraph.html
.. [3] https://en.wikipedia.org/wiki/Hoffman%E2%80%93Singleton_graph

rQ   pentagonr5   	pentagramrE   zHoffman-Singleton Graph)r'   Graphr9   r:   convert_node_labels_to_integersr6   )r+   r@   jks       r-   r   r     s    : 	
A1XqAJJ
A)JEQ;+GHJJ
A)JEQ;+GHJJQ*[!!eq[,IJJJQ*[!!eq[,IJ1X

J-QQa/PQ    	**1-A&AFHr0   c                 ^    [         R                  " SS/SS// SQ/ SQSS/S.U S9nS	Ul        U$ )
a  
Returns the House graph (square with triangle on top)

The house graph is a simple undirected graph with
5 nodes and 6 edges [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    House graph in the form of a square with a triangle on top

References
----------
.. [1] https://mathworld.wolfram.com/HouseGraph.html
r5   rE   r   rG   )r   rG   rH   r5   rE   rH   rI   r$   zHouse GraphrJ   rL   s     r-   r   r     s?    . 	F1v)	q!fE!	A AFHr0   c                 P    [        U 5      nUR                  SS/5        SUl        U$ )a]  
Returns the House graph with a cross inside the house square.

The House X-graph is the House graph plus the two edges connecting diagonally
opposite vertices of the square base. It is also one of the two graphs
obtained by removing two edges from the pentatope graph [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    House graph with diagonal vertices connected

References
----------
.. [1] https://mathworld.wolfram.com/HouseGraph.html
)r   rG   )r5   rE   zHouse-with-X-inside Graph)r   rb   r6   rL   s     r-   r   r      s-    0 	L!Aff%&(AFHr0   c                 v    [         R                  " / SQ/ SQ/ SQ/ SQ/ SQSS// SQS	/S
/S/S.
U S9nSUl        U$ )a)  
Returns the Platonic Icosahedral graph.

The icosahedral graph has 12 nodes and 30 edges. It is a Platonic graph
whose nodes have the connectivity of the icosahedron. It is undirected,
regular and Hamiltonian [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Icosahedral graph with 12 nodes and 30 edges.

References
----------
.. [1] https://mathworld.wolfram.com/IcosahedralGraph.html
)r5   rQ   rR   rS   rU   )rE   rQ   rN   rS   )rG   rN   rS   rO   )rH   rN   rO   rT   )rQ   rN   rT   rU   rN   rU   )rS   rO   rT   rU   rO   rT   )
r   r5   rE   rG   rH   rQ   rR   rS   rO   rT   r$   zPlatonic Icosahedral GraphrJ   rL   s     r-   r   r     sT    0 	2wst	
 "	A *AFHr0   c                 z    [         R                  " / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQS	S
/S/S.
U S9nSUl        U$ )u  
Returns the Krackhardt Kite Social Network.

A 10 actor social network introduced by David Krackhardt
to illustrate different centrality measures [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Krackhardt Kite graph with 10 nodes and 18 edges

Notes
-----
The traditional labeling is:
Andre=1, Beverley=2, Carol=3, Diane=4,
Ed=5, Fernando=6, Garth=7, Heather=8, Ike=9, Jane=10.

References
----------
.. [1] Krackhardt, David. "Assessing the Political Landscape: Structure,
   Cognition, and Power in Organizations". Administrative Science Quarterly.
   35 (2): 342–369. doi:10.2307/2393394. JSTOR 2393394. June 1990.

)r5   rE   rG   rQ   )r   rG   rH   rN   )r   rG   rQ   )r   r5   rE   rH   rQ   rN   rX   )r   rE   rG   rN   rR   )r5   rG   rH   rQ   rR   )rQ   rN   rS   rR   rO   rS   rV   r$   zKrackhardt Kite Social NetworkrJ   rL   s     r-   r   r   I  sQ    @ 	!1vs	
 "	A .AFHr0   c                 4    [        SSS/SU 5      nSUl        U$ )u  
Returns the Moebius-Kantor graph.

The Möbius-Kantor graph is the cubic symmetric graph on 16 nodes.
Its LCF notation is [5,-5]^8, and it is isomorphic to the generalized
Petersen graph [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Moebius-Kantor graph

References
----------
.. [1] https://en.wikipedia.org/wiki/M%C3%B6bius%E2%80%93Kantor_graph

   rQ   r[   rS   zMoebius-Kantor Graphr\   rL   s     r-   r   r   |  s$    0 	"q"gq,/A#AFHr0   c                 \    [         R                  " / SQ/ SQSS/SS/S/S.U S9nSUl        U$ )a  
Returns the Platonic Octahedral graph.

The octahedral graph is the 6-node 12-edge Platonic graph having the
connectivity of the octahedron [1]_. If 6 couples go to a party,
and each person shakes hands with every person except his or her partner,
then this graph describes the set of handshakes that take place;
for this reason it is also called the cocktail party graph [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Octahedral graph

References
----------
.. [1] https://mathworld.wolfram.com/OctahedralGraph.html
.. [2] https://en.wikipedia.org/wiki/Tur%C3%A1n_graph#Special_cases

)r5   rE   rG   rH   )rE   rG   rQ   rH   rQ   rI   r$   zPlatonic Octahedral GraphrJ   rL   s     r-   r   r     s=    8 	YAq6q!f!E!	A )AFHr0   c                  2    [        S/ SQS5      n SU l        U $ )aH  
Returns the Pappus graph.

The Pappus graph is a cubic symmetric distance-regular graph with 18 nodes
and 27 edges. It is Hamiltonian and can be represented in LCF notation as
[5,7,-7,7,-7,-5]^3 [1]_.

Returns
-------
G : networkx Graph
    Pappus graph

References
----------
.. [1] https://en.wikipedia.org/wiki/Pappus_graph
   )rQ   rR   r`   rR   r`   r[   rG   zPappus Graphr\   )r+   s    r-   r   r     s    $ 	"+Q/AAFHr0   c                 |    [         R                  " / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ S	Q/ S
QS.
U S9nSUl        U$ )a  
Returns the Petersen graph.

The Peterson graph is a cubic, undirected graph with 10 nodes and 15 edges [1]_.
Julius Petersen constructed the graph as the smallest counterexample
against the claim that a connected bridgeless cubic graph
has an edge colouring with three colours [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Petersen graph

References
----------
.. [1] https://en.wikipedia.org/wiki/Petersen_graph
.. [2] https://www.win.tue.nl/~aeb/drg/graphs/Petersen.html
)r5   rH   rQ   )r   rE   rN   )r5   rG   rR   )rE   rH   rS   )rG   r   rO   )r   rR   rS   )r5   rS   rO   )rE   rQ   rO   )rG   rQ   rN   )rH   rN   rR   rV   r$   zPetersen GraphrJ   rL   s     r-   r   r     sJ    4 		
 "	A AFHr0   c                 $   [        SU 5      nUR                  [        S5      5        UR                  SS/SS/SS//5        UR                  SS/SS//5        UR                  SS	/SS//5        UR                  S	S/S	S/S	S//5        S
Ul        U$ )a  
Return a small maze with a cycle.

This is the maze used in Sedgewick, 3rd Edition, Part 5, Graph
Algorithms, Chapter 18, e.g. Figure 18.2 and following [1]_.
Nodes are numbered 0,..,7

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Small maze with a cycle

References
----------
.. [1] Figure 18.2, Chapter 18, Graph Algorithms (3rd Ed), Sedgewick
r   rS   rE   rR   rQ   r5   rN   rG   rH   zSedgewick Maze)r   add_nodes_fromr9   rb   r6   rL   s     r-   r   r     s    . 	A|$AU1Xq!fq!fq!f-.q!fq!f%&q!fq!f%&q!fq!fq!f-.AFHr0   c                 ,    [        SU 5      nSUl        U$ )a  
Returns the 3-regular Platonic Tetrahedral graph.

Tetrahedral graph has 4 nodes and 6 edges. It is a
special case of the complete graph, K4, and wheel graph, W4.
It is one of the 5 platonic graphs [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Tetrahedral Graph

References
----------
.. [1] https://en.wikipedia.org/wiki/Tetrahedron#Tetrahedral_graph

rH   zPlatonic Tetrahedral Graph)r   r6   rL   s     r-   r   r   "  s    0 	q,'A)AFHr0   c           
          [         R                  " 0 S/ SQ_SSS/_SSS/_SS	S
/_SS/_SSS/_S	SS
/_SSS/_S
S/_SSS/_SSS/_SS/_SS/_SSS/_SS/_SSS/_SSS/_S/S/S/S/S/S/S.EU S9nSUl        U$ )a  
Returns the skeleton of the truncated cube.

The truncated cube is an Archimedean solid with 14 regular
faces (6 octagonal and 8 triangular), 36 edges and 24 nodes [1]_.
The truncated cube is created by truncating (cutting off) the tips
of the cube one third of the way into each edge [2]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Skeleton of the truncated cube

References
----------
.. [1] https://en.wikipedia.org/wiki/Truncated_cube
.. [2] https://www.coolmath.com/reference/polyhedra-truncated-cube

r   rm   r5   rU   rd   rE   rG   rH   rN   rS   rQ   rr   ru   rR   rT      rO      rZ                     )r|   ru   r   rZ   r~   r   r$   zTruncated Cube GraphrJ   rL   s     r-   r   r   ?  sO   6 		
y	
Bx	
 1v	
 1v		

 s	
 Bx	
 1v	
 Bx	
 s	
 Bx	
 R	
 	
 	
 R	
 	
  R!	
" R#	
$ /	
2 "5	A8 $AFHr0   c                 R    [        SU 5      nUR                  / SQ5        SUl        U$ )a  
Returns the skeleton of the truncated Platonic tetrahedron.

The truncated tetrahedron is an Archimedean solid with 4 regular hexagonal faces,
4 equilateral triangle faces, 12 nodes and 18 edges. It can be constructed by truncating
all 4 vertices of a regular tetrahedron at one third of the original edge length [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Skeleton of the truncated tetrahedron

References
----------
.. [1] https://en.wikipedia.org/wiki/Truncated_tetrahedron

r{   ))r   rE   )r   rO   )r5   rN   )rG   rU   )rH   rU   )rQ   rR   )rS   rT   zTruncated Tetrahedron Graph)r    rb   r6   rL   s     r-   r   r   z  s+    0 	2|$APQ*AFHr0   c           
         [         R                  " 0 S/ SQ_SSS/_SSS/_S	S
S/_SSS/_SSS/_SSS/_SSS/_SSS/_SSS/_SS/_SSS/_SSS/_SSS/_SS/_SSS/_SSS /_0 SS
S!/_S
S"/_SS#S"/_S#S$S%/_S$SS&/_SS'/_S&S(S/_S(S)S*/_S)SS+/_SS/_SS,/_S,SS*/_SS-/_S-S+S/_S+S*/_SSS/_SS./_ESS/S/S%S /S//S!S"/S /S0.EU S19nS2Ul        U$ )3ah  
Returns the Tutte graph.

The Tutte graph is a cubic polyhedral, non-Hamiltonian graph. It has
46 nodes and 69 edges.
It is a counterexample to Tait's conjecture that every 3-regular polyhedron
has a Hamiltonian cycle.
It can be realized geometrically from a tetrahedron by multiply truncating
three of its vertices [1]_.

Parameters
----------
create_using : NetworkX graph constructor, optional (default=nx.Graph)
   Graph type to create. If graph instance, then cleared before populated.

Returns
-------
G : networkx Graph
    Tutte graph

References
----------
.. [1] https://en.wikipedia.org/wiki/Tutte_graph
r   )r5   rE   rG   r5   rH      rE   rT   rU   rG   ru   r   rQ   !   rN      rR      rS   rd   rO   &   %   '   r{   r}   #   r   "   rr   r   r|   ,   +   -   rZ   r~   )   r   (                      $   *   )r   r   r   r   r   r   r$   zTutte's GraphrJ   rL   s     r-   r   r     sh   6 	)	
y)	
2w)	
 Bx)	
 Bx	)	

 2w)	
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 2w)	
 2w)	
 2w)	
 Bx)	
 )	
 R)	
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 R)	
 )	
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$ R%)	
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, R-)	
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@ A)	
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D E)	
F RRRQ)	
T "W,	AZ AFHr0   )N)&__doc____all__	functoolsr   networkxr'   networkx.exceptionr   networkx.generators.classicr   r   r   r    r1   _dispatchabler   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r0   r-   <module>r      s  
4   , $ T2H 3H` T2 3 @ T2( 3 (V T2' 3 'T T2 3: T2 3 8 T2 3< T2+ 3+\ T2 3B T2' 3'T T2 3 : T2 3 8 T2& 3 &R T2. 3 .b T2 38 T2 3 D T2 3, T2( 3 (V T2 3@ T2 38 T26 3 6r T2 3: T2G 3 Gr0   