o
    ]Zh                     @   sp   d Z ddlZddlmZ g dZejdd Zedejdd	 Zeded
ejddddddZ	dS )z5Functions for computing and verifying regular graphs.    N)not_implemented_for)
is_regularis_k_regulark_factorc                    s   t | dkrtdtj| }|  s&| | t fdd| jD S | |tfdd| jD }| 	|tfdd| j	D }|oK|S )a  Determines whether the graph ``G`` is a regular graph.

    A regular graph is a graph where each vertex has the same degree. A
    regular digraph is a graph where the indegree and outdegree of each
    vertex are equal.

    Parameters
    ----------
    G : NetworkX graph

    Returns
    -------
    bool
        Whether the given graph or digraph is regular.

    Examples
    --------
    >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 1)])
    >>> nx.is_regular(G)
    True

    r   zGraph has no nodes.c                 3       | ]	\}} |kV  qd S N .0_d)d1r   J/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/regular.py	<genexpr>&       zis_regular.<locals>.<genexpr>c                 3   r   r   r   r	   )d_inr   r   r   )   r   c                 3   r   r   r   r	   )d_outr   r   r   +   r   )
lennxZNetworkXPointlessConceptutilsZarbitrary_elementZis_directeddegreeallZ	in_degreeZ
out_degree)GZn1Z
in_regularZout_regularr   )r   r   r   r   r   	   s   



r   Zdirectedc                    s   t  fdd| jD S )a  Determines whether the graph ``G`` is a k-regular graph.

    A k-regular graph is a graph where each vertex has degree k.

    Parameters
    ----------
    G : NetworkX graph

    Returns
    -------
    bool
        Whether the given graph is k-regular.

    Examples
    --------
    >>> G = nx.Graph([(1, 2), (2, 3), (3, 4), (4, 1)])
    >>> nx.is_k_regular(G, k=3)
    False

    c                 3   s    | ]	\}}| kV  qd S r   r   )r
   nr   kr   r   r   F   r   zis_k_regular.<locals>.<genexpr>)r   r   )r   r   r   r   r   r   /   s   r   Z
multigraphT)Zpreserve_edge_attrsZreturns_graphweightc                    s$  ddl m}m} G  fddd}G dd d}tfdd| jD r)td	|   g }t jD ]"\}}	|	d
 k rF||	| }
n||	| }
|
	  |
|
 q4| d|d}| |shtd  D ]}||vr|d |d f|vr |d |d  ql|D ]}
|
  q S )u  Compute a k-factor of G

    A k-factor of a graph is a spanning k-regular subgraph.
    A spanning k-regular subgraph of G is a subgraph that contains
    each vertex of G and a subset of the edges of G such that each
    vertex has degree k.

    Parameters
    ----------
    G : NetworkX graph
      Undirected graph

    matching_weight: string, optional (default='weight')
       Edge data key corresponding to the edge weight.
       Used for finding the max-weighted perfect matching.
       If key not found, uses 1 as weight.

    Returns
    -------
    G2 : NetworkX graph
        A k-factor of G

    Examples
    --------
    >>> G = nx.Graph([(1, 2), (2, 3), (3, 4), (4, 1)])
    >>> G2 = nx.k_factor(G, k=1)
    >>> G2.edges()
    EdgeView([(1, 2), (3, 4)])

    References
    ----------
    .. [1] "An algorithm for computing simple k-factors.",
       Meijer, Henk, Yurai Núñez-Rodríguez, and David Rappaport,
       Information processing letters, 2009.
    r   )is_perfect_matchingmax_weight_matchingc                       s(   e Zd Zdd Zdd Z fddZdS )zk_factor.<locals>.LargeKGadgetc                    sR   | _ || _|| _ | _fddt D | _ fddt | D | _d S )Nc                       g | ]} |fqS r   r   r
   xnoder   r   
<listcomp>z       z;k_factor.<locals>.LargeKGadget.__init__.<locals>.<listcomp>c                       g | ]}|  fqS r   r   r    r   r#   r   r   r$   {       )originalgr   r   rangeouter_verticescore_verticesselfr   r   r#   r*   r   r'   r   __init__t   s   "z'k_factor.<locals>.LargeKGadget.__init__c                 S   s   | j | j }t| }t| }t| j||D ]\}}}| j j||fi | q| jD ]}| jD ]	}| j || q2q-| j 	| j d S r   )
r*   r)   listkeysvalueszipr,   add_edger-   remove_node)r/   adj_viewZ	neighbors
edge_attrsouterneighborcorer   r   r   replace_node}   s   

z+k_factor.<locals>.LargeKGadget.replace_nodec                    s|   | j | j | jD ]%}| j | }t| D ]\}}|| jvr.| j j| j|fi |  nqq
 | j  | j d S r   )	r*   add_noder)   r,   r1   itemsr-   r5   remove_nodes_fromr/   r9   r7   r:   r8   r*   r   r   restore_node   s   


z+k_factor.<locals>.LargeKGadget.restore_nodeN__name__
__module____qualname__r0   r<   rB   r   rA   r   r   LargeKGadgets   s    	rG   c                   @   s$   e Zd Zdd Zdd Zdd ZdS )zk_factor.<locals>.SmallKGadgetc                    sh   | _ || _ | _|| _fddt D | _ fddt D | _ fddt|D | _d S )Nc                    r   r   r   r    r"   r   r   r$      r%   z;k_factor.<locals>.SmallKGadget.__init__.<locals>.<listcomp>c                    r&   r   r   r    r'   r   r   r$      r(   c                    s   g | ]
}|d    fqS )   r   r    r'   r   r   r$      s    )r)   r   r   r*   r+   r,   inner_verticesr-   r.   r   r'   r   r0      s   z'k_factor.<locals>.SmallKGadget.__init__c                 S   s   | j | j }t| j| jt| D ]\}}\}}| j || | j j||fi | q| jD ]}| jD ]	}| j || q4q/| j 	| j d S r   )
r*   r)   r4   r,   rI   r1   r>   r5   r-   r6   )r/   r7   r9   innerr:   r8   r;   r   r   r   r<      s   

z+k_factor.<locals>.SmallKGadget.replace_nodec                 S   s   | j | j | jD ]#}| j | }| D ]\}}|| jvr,| j j| j|fi |  nqq
| j | j | j | j | j | j d S r   )	r*   r=   r)   r,   r>   r-   r5   r?   rI   r@   r   r   r   rB      s   


z+k_factor.<locals>.SmallKGadget.restore_nodeNrC   r   r   r   r   SmallKGadget   s    
rK   c                 3   s    | ]	\}}| k V  qd S r   r   r	   r   r   r   r      r   zk_factor.<locals>.<genexpr>z/Graph contains a vertex with degree less than kg       @T)Zmaxcardinalityr   z7Cannot find k-factor because no perfect matching exists   )Znetworkx.algorithms.matchingr   r   anyr   r   ZNetworkXUnfeasiblecopyr1   r<   appendedgesZremove_edgerB   )r   r   Zmatching_weightr   r   rG   rK   Zgadgetsr#   r   ZgadgetZmatchingedger   )r*   r   r   r   I   s2   ("$


r   )r   )
__doc__Znetworkxr   Znetworkx.utilsr   __all__Z_dispatchabler   r   r   r   r   r   r   <module>   s    
%