R/centrality-batch12.R

In cograph: Analysis and Visualization of Complex Networks

#' Calculate topology-only measures from the parameter-candidate list
#' @keywords internal
#' @noRd
calculate_candidate_local <- function(cg, measure, mdd_lambda = 0.7) {
  b <- .cg_undirected_view(.cg_path_matrix(cg, NULL))
  diag(b) <- 0
  switch(measure,
         truss = .cg_truss(b),
         mdd = .cg_mdd(b, mdd_lambda),
         .cg_local_candidates(b, measure))
}

#' Truss, mixed-degree decomposition and local social-capital measures
#'
#' Five measures with explicit definitions and numerical reference checks.
#' All use the simple, unweighted, undirected skeleton: either direction
#' creates an edge, parallel edges count once and self-loops are removed.
#' This projection is a cograph input convention; no directed or weighted
#' generalization of the published measures is claimed. All isolates score 0.
#'
#' \describe{
#'   \item{\code{truss}}{Maximum truss number of an incident edge
#'     (Malliaros et al. 2016). A k-truss requires at least k-2 triangles
#'     per edge within the surviving subgraph, matching NetworkX. An edge
#'     outside any triangle has truss number 2; a complete graph on k
#'     vertices has node truss number k. Some sources instead label by the
#'     triangle threshold, producing values two smaller.}
#'   \item{\code{mdd}}{Mixed-degree decomposition (Zeng & Zhang 2013):
#'     repeatedly peel by residual degree plus \code{mdd_lambda} times
#'     exhausted degree. Nodes falling below the current shell threshold
#'     join that shell before the threshold advances. Zero recovers the
#'     k-core number; one recovers degree. Intermediate thresholds are
#'     real-valued. Default 0.7, as in the paper's worked example.}
#'   \item{\code{bridging_coefficient}}{Hwang et al.'s reciprocal-degree
#'     ratio: \eqn{(1/d_i) / \sum_{j \in N(i)} 1/d_j}. This is the
#'     coefficient itself, before multiplication by betweenness.}
#'   \item{\code{godfather}}{Jackson's Godfather index: the number of
#'     unordered pairs of neighbors with no edge between them. Equals
#'     \eqn{d_i(d_i-1)/2} minus the number of triangles containing i.}
#'   \item{\code{support}}{Jackson's supported relationships: the number
#'     of neighbors sharing at least one common neighbor with i. An
#'     edge is counted once even if it belongs to multiple triangles.}
#' }
#'
#' LocalRank (Chen et al. 2012), also listed in the Centrality Zoo, is
#' already available as \code{\link{centrality_semilocal}} on an
#' undirected, unweighted graph; it needs no additional numerical function.
#'
#' @param x Network input accepted by \code{\link{centrality}}.
#' @param mdd_lambda Exhausted-degree weight between 0 and 1, default 0.7.
#' @param ... Additional arguments to \code{\link{centrality}}. With
#'   \code{normalized = TRUE}, positive scores are divided by their maximum.
#' @return Named numeric vector in input node order.
#' @references
#' Malliaros, F. D., Rossi, M. E. G., & Vazirgiannis, M. (2016).
#' Locating influential nodes in complex networks. Scientific Reports, 6,
#' 19307. \doi{10.1038/srep19307}.
#'
#' Zeng, A., & Zhang, C. J. (2013). Ranking spreaders by decomposing complex
#' networks. Physics Letters A, 377, 1031-1035.
#' \doi{10.1016/j.physleta.2013.02.039}.
#'
#' Hwang, W., Kim, T., Ramanathan, M., & Zhang, A. (2008). Bridging
#' centrality: graph mining from element level to group level. KDD '08,
#' 336-344. \doi{10.1145/1401890.1401934}.
#'
#' Jackson, M. O. (2020). A typology of social capital and associated
#' network measures. Social Choice and Welfare, 54, 311-336.
#' \doi{10.1007/s00355-019-01189-3}.
#'
#' Chen, D., Lu, L., Shang, M. S., Zhang, Y. C., & Zhou, T. (2012).
#' Identifying influential nodes in complex networks. Physica A, 391,
#' 1777-1787. \doi{10.1016/j.physa.2011.09.017}.
#' @seealso \code{\link{list_centralities}},
#'   \code{\link{centrality_coreness}}, \code{\link{centrality_bridging}}.
#' @export
#' @examples
#' adj <- matrix(1, 4, 4)
#' diag(adj) <- 0
#' centrality_truss(adj)
#' centrality_mdd(adj, mdd_lambda = 0.7)
#' centrality_support(adj)
centrality_truss <- function(x, ...) {
  df <- centrality(x, measures = "truss", ...)
  stats::setNames(df$truss, df$node)
}

#' @rdname centrality_truss
#' @export
centrality_mdd <- function(x, mdd_lambda = 0.7, ...) {
  df <- centrality(x, measures = "mdd", mdd_lambda = mdd_lambda, ...)
  stats::setNames(df$mdd, df$node)
}

#' @rdname centrality_truss
#' @export
# nolint start: object_length_linter.
centrality_bridging_coefficient <- function(x, ...) {
  df <- centrality(x, measures = "bridging_coefficient", ...)
  stats::setNames(df$bridging_coefficient, df$node)
}
# nolint end: object_length_linter.

#' @rdname centrality_truss
#' @export
centrality_godfather <- function(x, ...) {
  df <- centrality(x, measures = "godfather", ...)
  stats::setNames(df$godfather, df$node)
}

#' @rdname centrality_truss
#' @export
centrality_support <- function(x, ...) {
  df <- centrality(x, measures = "support", ...)
  stats::setNames(df$support, df$node)
}