R/centrality-batch23.R

In cograph: Analysis and Visualization of Complex Networks

#' Calculate adaptive LeaderRank using original graph H-indices
#' @keywords internal
#' @noRd
calculate_adaptive_leaderrank <- function(cg, h_mode = "all") {
  b <- .cg_path_matrix(cg, NULL)
  diag(b) <- 0
  .cg_adaptive_leaderrank(b, h_mode)
}

#' Adaptive LeaderRank centrality
#'
#' Xu and Wang's adaptive LeaderRank computes original node H-indices,
#' then adds a ground node with H-index one, joined bidirectionally to
#' every original node. Each augmented arc from j to i has weight
#' \eqn{a_{ji}h_i}. Row-normalized weights define the resource transition
#' matrix. Raw stationary scores retain total augmented mass N, following
#' initial score one on ordinary nodes and zero on ground. The ground
#' score is omitted without redistribution. H-indices are not recomputed
#' after ground edges are added.
#'
#' The H-index is the largest integer h for which at least h original
#' neighbors have degree at least h. The focal node is excluded from that
#' neighbor list. This differs from cograph's existing closed-neighborhood
#' \code{\link{centrality_lobby}} convention.
#'
#' The paper evaluates directed and undirected networks but does not pin
#' a directed H-index convention. \code{alr_h_mode} makes that choice
#' explicit. Default \code{"all"} computes H-indices on the simple
#' undirected skeleton, merging reciprocal arcs. \code{"out"} uses outgoing
#' neighbors' out-degrees; \code{"in"} uses incoming neighbors' in-degrees.
#' These directed H-index choices are explicit cograph conventions, not
#' claims of the authors' directed-software behavior. In every case, resource
#' flow retains the original directed arcs. Undirected edges become opposite
#' arcs, and all H-index modes then coincide.
#'
#' Input weights are ignored; the algorithm generates its own destination
#' weights. Loops are removed and parallel arcs count once. The generic
#' \code{mode}, inversion and cutoff arguments are ignored. Original nodes
#' with H-index zero receive zero stationary score. If every H-index is zero,
#' the ground transition row is undefined and all scores are NaN. This can
#' occur on edgeless inputs or some directed inputs in in/out H-index modes.
#' Empty input returns an empty vector. No H-index pseudocount is added.
#'
#' A native ground-elimination solve obtains the unique stationary solution
#' in O(N^3) time and O(N^2) memory, including periodic chains for which
#' ordinary iteration need not converge. Optional final max normalization
#' acts on the returned ordinary-node scores. Numerical definition agreement
#' does not establish superior spreading predictions or author-code parity.
#'
#' @param x Network input accepted by \code{\link{centrality}}.
#' @param alr_h_mode Original H-index convention: all (default), out or in.
#' @param ... Additional arguments to \code{\link{centrality}}.
#' @return Named numeric vector in input node order.
#' @references
#' Xu, S., & Wang, P. (2017). Identifying important nodes by adaptive
#'   LeaderRank. Physica A, 469, 654-664. \doi{10.1016/j.physa.2016.11.034}.
#' @export
#' @examplesIf requireNamespace("igraph", quietly = TRUE)
#' centrality_adaptive_leaderrank(igraph::make_ring(4))
centrality_adaptive_leaderrank <- function(x, alr_h_mode = "all", ...) {
  df <- centrality(x, measures = "adaptive_leaderrank",
                   alr_h_mode = alr_h_mode, ...)
  stats::setNames(df$adaptive_leaderrank, df$node)
}