def reset_local_connectivity(simplicial_set):
    """Reset the local connectivity requirement -- each data sample should
    have complete confidence in at least one 1-simplex in the simplicial set.
    We can enforce this by locally rescaling confidences, and then remerging the
    different local simplicial sets together.

    Parameters
    ----------
    simplicial_set: sparse matrix
        The simplicial set for which to recalculate with respect to local
        connectivity.

    Returns
    -------
    simplicial_set: sparse_matrix
        The recalculated simplicial set, now with the local connectivity
        assumption restored.
    """
    simplicial_set = normalize(simplicial_set, norm="max")
    transpose = simplicial_set.transpose()
    prod_matrix = simplicial_set.multiply(transpose)
    simplicial_set = simplicial_set + transpose - prod_matrix
    simplicial_set.eliminate_zeros()

    return simplicial_set