#' @details
#'
#' @section Triad censuses: Three triad censuses are implemented for affiliation
#' networks:
#' \itemize{
#' \item The \emph{full triad census} (Brunson, 2015) records the number of
#' triads of each isomorphism class. The classes are indexed by a partition,
#' \eqn{\lambda=(\lambda_1\leq\lambda_2\leq\lambda_3)}, indicating the number
#' of events attended by both actors in each pair but not the third, and a
#' positive integer, \eqn{w}, indicating the number of events attended by all
#' three actors. The isomorphism classes are organized into a matrix with rows
#' indexed by \eqn{\lambda} and columns indexed by \eqn{w}, with the
#' partitions \eqn{\lambda} ordered according to the \emph{revolving door
#' ordering} (Kreher & Stinson, 1999). The main function
#' \code{\link{triad_census_an}} (called from \code{triad_census} when the
#' \code{graph} argument is an \code{affiliation_network}) defaults to this
#' census.
#' \item For the analysis of sparse affiliation networks, the full triad
#' census may be less useful than information on whether the extent of
#' connectivity through co-attended events differs between each pair of
#' actors. In order to summarize this information, a coarser triad census can
#' be conducted on classes of triads based on the following congruence
#' relation: Using the indices \eqn{\lambda=(x\ge y\ge z)} and \eqn{w}
#' above, note that the numbers of shared events for each pair and for the
#' triad are \eqn{x+w\ge y+w\ge z+w\ge w\ge 0}. Consider two triads
#' congruent if the same subset of these weak inequalities are strictly
#' satisfied. The resulting \emph{difference triad census}, previously called
#' the \emph{uniformity triad census}, implemented as
#' \code{\link{triad_census_difference}}, is organized into a \eqn{8\times 2}
#' matrix with the strictness of the first three inequalities determining the
#' row and that of the last inequality determining the column.
#' \item A still coarser congruence relation can be used to tally how many are
#' connected by at least one event in each distinct way. This relation
#' considers two triads congruent if each corresponding pair of actors both
#' attended or did not attend at least one event not attended by the third,
#' and if the corresponding triads both attended or did not attend at least
#' one event together. The \emph{binary triad census} (Brunson, 2015; therein
#' called the \emph{structural triad census}), implemented as
#' \code{\link{triad_census_binary}}, records the number of triads in each
#' congruence class.
#' \item The \emph{simple triad census} is the 4-entry triad census on a
#' traditional (non-affiliation) network indicating the number of triads of
#' each isomorphism class, namely whether the triad contains zero, one, two,
#' or three links. The function \code{\link{simple_triad_census}} computes the
#' classical (undirected) triad census for an undirected traditional network,
#' or for the actor projection of an affiliation network (if provided), using
#' \code{\link[igraph]{triad_census}}; if the result doesn't make sense (i.e.,
#' the sum of the entries is not the number of triples of nodes), then it
#' instead uses its own, much slower method.
#' }
#' Each of these censuses can be projected from the previous using the
#' function \code{\link{project_census}}. A fourth census, called the
#' \emph{uniformity triad census} and implemented as
#' \code{\link{unif_triad_census}}, is deprecated. Three-actor triad
#' affiliation networks can be constructed and plotted using the
#' \code{\link{triad}} functions.
#'
#' The default method for the two affiliation network--specific triad censuses
#' is adapted from the algorithm of Batagelj and Mrvar (2001) for calculating
#' the classical triad census for a directed graph.
#'
#' @references
#'
#' Kreher, D.L., & Stinson, D.R. (1999). Combinatorial algorithms: generation,
#' enumeration, and search. \emph{SIGACT News}, 30(1), 33--35.
#'
#' Batagelj, V., & Mrvar, A. (2001). A subquadratic triad census algorithm for
#' large sparse networks with small maximum degree. \emph{Social Networks},
#' 23(3), 237--243.
#'
#' Brunson, J.C. (2015). Triadic analysis of affiliation networks. \emph{Network
#' Science}, 3(4), 480--508.
#'
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