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    ˷eH                     @   s(   d Z ddlZddgZdd Zdd ZdS )z$
Utilities for connectivity package
    N!build_auxiliary_node_connectivity!build_auxiliary_edge_connectivityc           	      C   s   |   }i }t }t| D ]*\}}|||< |j| d|d |j| d|d |j| d| ddd qg }|  D ](\}}|||  d||  df |sg|||  d||  df q?|j|dd ||j	d< |S )a/  Creates a directed graph D from an undirected graph G to compute flow
    based node connectivity.

    For an undirected graph G having `n` nodes and `m` edges we derive a
    directed graph D with `2n` nodes and `2m+n` arcs by replacing each
    original node `v` with two nodes `vA`, `vB` linked by an (internal)
    arc in D. Then for each edge (`u`, `v`) in G we add two arcs (`uB`, `vA`)
    and (`vB`, `uA`) in D. Finally we set the attribute capacity = 1 for each
    arc in D [1]_.

    For a directed graph having `n` nodes and `m` arcs we derive a
    directed graph D with `2n` nodes and `m+n` arcs by replacing each
    original node `v` with two nodes `vA`, `vB` linked by an (internal)
    arc (`vA`, `vB`) in D. Then for each arc (`u`, `v`) in G we add one
    arc (`uB`, `vA`) in D. Finally we set the attribute capacity = 1 for
    each arc in D.

    A dictionary with a mapping between nodes in the original graph and the
    auxiliary digraph is stored as a graph attribute: H.graph['mapping'].

    References
    ----------
    .. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and
        Erlebach, 'Network Analysis: Methodological Foundations', Lecture
        Notes in Computer Science, Volume 3418, Springer-Verlag, 2005.
        https://doi.org/10.1007/978-3-540-31955-9_7

    A)idB   capacitymapping)
is_directednxDiGraph	enumerateadd_nodeadd_edgeedgesappendadd_edges_fromgraph)	Gdirectedr
   Hinoder   sourcetarget r   ]/var/www/ideatree/venv/lib/python3.10/site-packages/networkx/algorithms/connectivity/utils.pyr   	   s"   ""
c                 C   sz   |   rt }||   |j|  dd |S t }||   |  D ]\}}|j||f||fgdd q)|S )aR  Auxiliary digraph for computing flow based edge connectivity

    If the input graph is undirected, we replace each edge (`u`,`v`) with
    two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute
    'capacity' for each arc to 1. If the input graph is directed we simply
    add the 'capacity' attribute. Part of algorithm 1 in [1]_ .

    References
    ----------
    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. (this is a
        chapter, look for the reference of the book).
        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
    r   r   )r   r   r   add_nodes_fromnodesr   r   )r   r   r   r   r   r   r   r   =   s   )__doc__networkxr   __all__r   r   r   r   r   r   <module>   s
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