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z% Computation of graph non-randomness
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| ¡ƒƒ}|j tj| |d¡}| | |d|… ¡¡}|  ¡ }|  ¡ }d| | |||   }||d|  | |  t d| | d|  ¡ }	||	fS )a‚  Compute the non-randomness of graph G.

    The first returned value nr is the sum of non-randomness values of all
    edges within the graph (where the non-randomness of an edge tends to be
    small when the two nodes linked by that edge are from two different
    communities).

    The second computed value nr_rd is a relative measure that indicates
    to what extent graph G is different from random graphs in terms
    of probability. When it is close to 0, the graph tends to be more
    likely generated by an Erdos Renyi model.

    Parameters
    ----------
    G : NetworkX graph
        Graph must be symmetric, connected, and without self-loops.

    k : int
        The number of communities in G.
        If k is not set, the function will use a default community
        detection algorithm to set it.

    weight : string or None, optional (default=None)
        The name of an edge attribute that holds the numerical value used
        as a weight. If None, then each edge has weight 1, i.e., the graph is
        binary.

    Returns
    -------
    non-randomness : (float, float) tuple
        Non-randomness, Relative non-randomness w.r.t.
        Erdos Renyi random graphs.

    Raises
    ------
    NetworkXException
        if the input graph is not connected.
    NetworkXError
        if the input graph contains self-loops.

    Examples
    --------
    >>> G = nx.karate_club_graph()
    >>> nr, nr_rd = nx.non_randomness(G, 2)
    >>> nr, nr_rd = nx.non_randomness(G, 2, 'weight')

    Notes
    -----
    This computes Eq. (4.4) and (4.5) in Ref. [1]_.

    If a weight field is passed, this algorithm will use the eigenvalues
    of the weighted adjacency matrix to compute Eq. (4.4) and (4.5).

    References
    ----------
    .. [1] Xiaowei Ying and Xintao Wu,
           On Randomness Measures for Social Networks,
           SIAM International Conference on Data Mining. 2009
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