def rank_centrality(n_items, data, alpha=0.0):
    """Compute the Rank Centrality estimate of model parameters.

    This function implements Negahban et al.'s Rank Centrality algorithm
    [NOS12]_. The algorithm is similar to :func:`~choix.ilsr_pairwise`, but
    considers the *ratio* of wins for each pair (instead of the total count).

    The transition rates of the Rank Centrality Markov chain are initialized
    with ``alpha``. When ``alpha > 0``, this corresponds to a form of
    regularization (see :ref:`regularization` for details).

    Parameters
    ----------
    n_items : int
        Number of distinct items.
    data : list of lists
        Pairwise-comparison data.
    alpha : float, optional
        Regularization parameter.

    Returns
    -------
    params : numpy.ndarray
        An estimate of model parameters.
    """
    _, chain = _init_lsr(n_items, alpha, None)
    for winner, loser in data:
        chain[loser, winner] += 1.0
    # Transform the counts into ratios.
    idx = chain > 0  # Indices (i,j) of non-zero entries.
    chain[idx] = chain[idx] / (chain + chain.T)[idx]
    # Finalize the Markov chain by adding the self-transition rate.
    chain -= np.diag(chain.sum(axis=1))
    return log_transform(statdist(chain))
Compute the Rank Centrality estimate of model parameters.

    This function implements Negahban et al.'s Rank Centrality algorithm
    [NOS12]_. The algorithm is similar to :func:`~choix.ilsr_pairwise`, but
    considers the *ratio* of wins for each pair (instead of the total count).

    The transition rates of the Rank Centrality Markov chain are initialized
    with ``alpha``. When ``alpha > 0``, this corresponds to a form of
    regularization (see :ref:`regularization` for details).

    Parameters
    ----------
    n_items : int
        Number of distinct items.
    data : list of lists
        Pairwise-comparison data.
    alpha : float, optional
        Regularization parameter.

    Returns
    -------
    params : numpy.ndarray
        An estimate of model parameters.