R/centralization.R

In igraph/rigraph: Network Analysis and Visualization

#' Centralization of a graph
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralize.scores()` was renamed to [centralize()] to create a more
#' consistent API.
#' @inheritParams centralize
#' @keywords internal
#' @export
centralize.scores <- function(scores, theoretical.max = 0, normalized = TRUE) {
  # nocov start
  lifecycle::deprecate_soft("2.0.0", "centralize.scores()", "centralize()")
  centralize(
    scores = scores,
    theoretical.max = theoretical.max,
    normalized = normalized
  )
} # nocov end

#' Theoretical maximum for betweenness centralization
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.evcent.tmax()` was renamed to [centr_eigen_tmax()] to create a more
#' consistent API.
#' @inheritParams centr_eigen_tmax
#' @keywords internal
#' @export
centralization.evcent.tmax <- function(
  graph = NULL,
  nodes = 0,
  directed = FALSE,
  scale = TRUE
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.evcent.tmax()",
    "centr_eigen_tmax()"
  )
  centr_eigen_tmax(
    graph = graph,
    nodes = nodes,
    directed = directed,
    scale = scale
  )
} # nocov end

#' Centralize a graph according to the eigenvector centrality of vertices
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.evcent()` was renamed to [centr_eigen()] to create a more
#' consistent API.
#' @inheritParams centr_eigen
#' @keywords internal
#' @export
centralization.evcent <- function(
  graph,
  directed = FALSE,
  scale = TRUE,
  options = arpack_defaults(),
  normalized = TRUE
) {
  # nocov start
  lifecycle::deprecate_soft("2.0.0", "centralization.evcent()", "centr_eigen()")
  centr_eigen(
    graph = graph,
    directed = directed,
    scale = scale,
    options = options,
    normalized = normalized
  )
} # nocov end

#' Theoretical maximum for degree centralization
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.degree.tmax()` was renamed to [centr_degree_tmax()] to create a more
#' consistent API.
#' @inheritParams centr_degree_tmax
#' @keywords internal
#' @export
centralization.degree.tmax <- function(
  graph = NULL,
  nodes = 0,
  mode = c("all", "out", "in", "total"),
  loops = FALSE
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.degree.tmax()",
    "centr_degree_tmax()"
  )
  centr_degree_tmax(graph = graph, nodes = nodes, mode = mode, loops = loops)
} # nocov end

#' Centralize a graph according to the degrees of vertices
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.degree()` was renamed to [centr_degree()] to create a more
#' consistent API.
#' @inheritParams centr_degree
#' @keywords internal
#' @export
centralization.degree <- function(
  graph,
  mode = c("all", "out", "in", "total"),
  loops = TRUE,
  normalized = TRUE
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.degree()",
    "centr_degree()"
  )
  centr_degree(
    graph = graph,
    mode = mode,
    loops = loops,
    normalized = normalized
  )
} # nocov end

#' Theoretical maximum for closeness centralization
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.closeness.tmax()` was renamed to [centr_clo_tmax()] to create a more
#' consistent API.
#' @inheritParams centr_clo_tmax
#' @keywords internal
#' @export
centralization.closeness.tmax <- function(
  graph = NULL,
  nodes = 0,
  mode = c("out", "in", "all", "total")
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.closeness.tmax()",
    "centr_clo_tmax()"
  )
  centr_clo_tmax(graph = graph, nodes = nodes, mode = mode)
} # nocov end

#' Centralize a graph according to the closeness of vertices
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.closeness()` was renamed to [centr_clo()] to create a more
#' consistent API.
#' @inheritParams centr_clo
#' @keywords internal
#' @export
centralization.closeness <- function(
  graph,
  mode = c("out", "in", "all", "total"),
  normalized = TRUE
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.closeness()",
    "centr_clo()"
  )
  centr_clo(graph = graph, mode = mode, normalized = normalized)
} # nocov end

#' Theoretical maximum for betweenness centralization
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.betweenness.tmax()` was renamed to [centr_betw_tmax()] to create a more
#' consistent API.
#' @inheritParams centr_betw_tmax
#' @keywords internal
#' @export
centralization.betweenness.tmax <- function(
  graph = NULL,
  nodes = 0,
  directed = TRUE
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.betweenness.tmax()",
    "centr_betw_tmax()"
  )
  centr_betw_tmax(graph = graph, nodes = nodes, directed = directed)
} # nocov end

#' Centralize a graph according to the betweenness of vertices
#'
#' @description
#' `r lifecycle::badge("deprecated")`
#'
#' `centralization.betweenness()` was renamed to [centr_betw()] to create a more
#' consistent API.
#' @inheritParams centr_betw
#' @keywords internal
#' @export
centralization.betweenness <- function(
  graph,
  directed = TRUE,
  normalized = TRUE
) {
  # nocov start
  lifecycle::deprecate_soft(
    "2.0.0",
    "centralization.betweenness()",
    "centr_betw()"
  )
  centr_betw(graph = graph, directed = directed, normalized = normalized)
} # nocov end

## -----------------------------------------------------------------------
##
##   IGraph R package
##   Copyright (C) 2015  Gabor Csardi <csardi.gabor@gmail.com>
##   334 Harvard street, Cambridge, MA 02139 USA
##
##   This program is free software; you can redistribute it and/or modify
##   it under the terms of the GNU General Public License as published by
##   the Free Software Foundation; either version 2 of the License, or
##   (at your option) any later version.
##
##   This program is distributed in the hope that it will be useful,
##   but WITHOUT ANY WARRANTY; without even the implied warranty of
##   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##   GNU General Public License for more details.
##
##   You should have received a copy of the GNU General Public License
##   along with this program; if not, write to the Free Software
##   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
##   02110-1301 USA
##
## -----------------------------------------------------------------------

NULL

#' Centralization of a graph
#'
#' Centralization is a method for creating a graph level centralization
#' measure from the centrality scores of the vertices.
#'
#' Centralization is a general method for calculating a graph-level
#' centrality score based on node-level centrality measure. The formula for
#' this is
#' \deqn{C(G)=\sum_v (\max_w c_w - c_v),}{ C(G)=sum(max(c(w), w) - c(v), v),}
#' where \eqn{c_v}{c(v)} is the centrality of vertex \eqn{v}.
#'
#' The graph-level centralization measure can be normalized by dividing by the
#' maximum theoretical score for a graph with the same number of vertices,
#' using the same parameters, e.g. directedness, whether we consider loop
#' edges, etc.
#'
#' For degree, closeness and betweenness the most centralized structure is
#' some version of the star graph, in-star, out-star or undirected star.
#'
#' For eigenvector centrality the most centralized structure is the graph
#' with a single edge (and potentially many isolates).
#'
#' `centralize()` implements general centralization formula to calculate
#' a graph-level score from vertex-level scores.
#'
#' @param scores The vertex level centrality scores.
#' @param theoretical.max Real scalar. The graph-level centralization measure of
#'   the most centralized graph with the same number of vertices as the graph
#'   under study. This is only used if the `normalized` argument is set
#'   to `TRUE`.
#' @param normalized Logical scalar. Whether to normalize the graph level
#'   centrality score by dividing by the supplied theoretical maximum.
#' @return A real scalar, the centralization of the graph from which
#'   `scores` were derived.
#'
#' @aliases centralization
#' @family centralization related
#'
#' @export
#' @references Freeman, L.C.  (1979).  Centrality in Social Networks I:
#' Conceptual Clarification. *Social Networks* 1, 215--239.
#'
#' Wasserman, S., and Faust, K.  (1994).  *Social Network Analysis:
#' Methods and Applications.* Cambridge University Press.
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_degree(g)$centralization
#' centr_clo(g, mode = "all")$centralization
#' centr_eigen(g, directed = FALSE)$centralization
#'
#' # Calculate centralization from pre-computed scores
#' deg <- degree(g)
#' tmax <- centr_degree_tmax(g, loops = FALSE)
#' centralize(deg, tmax)
#'
#' # The most centralized graph according to eigenvector centrality
#' g0 <- make_graph(c(2, 1), n = 10, dir = FALSE)
#' g1 <- make_star(10, mode = "undirected")
#' centr_eigen(g0)$centralization
#' centr_eigen(g1)$centralization
#' @cdocs igraph_centralization
centralize <- centralization_impl

#' Centralize a graph according to the degrees of vertices
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph.
#' @param mode This is the same as the `mode` argument of
#'   `degree()`.
#' @param loops Logical scalar, whether to consider loops edges when
#'   calculating the degree.
#' @param normalized Logical scalar. Whether to normalize the graph level
#'   centrality score by dividing by the theoretical maximum.
#' @return A named list with the following components:
#'   \describe{
#'     \item{res}{
#'       The node-level centrality scores.
#'     }
#'     \item{centralization}{
#'       The graph level centrality index.
#'     }
#'     \item{theoretical_max}{
#'       The maximum theoretical graph level centralization score
#'       for a graph with the given number of vertices,
#'       using the same parameters.
#'       If the `normalized` argument was `TRUE`,
#'       then the result was divided by this number.
#'     }
#'   }
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_degree(g)$centralization
#' centr_clo(g, mode = "all")$centralization
#' centr_betw(g, directed = FALSE)$centralization
#' centr_eigen(g, directed = FALSE)$centralization
#' @cdocs igraph_centralization_degree
centr_degree <- centralization_degree_impl

#' Theoretical maximum for degree centralization
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph. It can also be `NULL` if `nodes` is given.
#' @param nodes The number of vertices. This is ignored if the graph is given.
#' @param mode This is the same as the `mode` argument of `degree()`. Ignored
#'   if `graph` is given and the graph is undirected.
#' @param loops Logical scalar, whether to consider loops edges when
#'   calculating the degree.
#' @return Real scalar, the theoretical maximum (unnormalized) graph degree
#'   centrality score for graphs with given order and other parameters.
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_degree(g, normalized = FALSE)$centralization %>%
#'   `/`(centr_degree_tmax(g, loops = FALSE))
#' centr_degree(g, normalized = TRUE)$centralization
centr_degree_tmax <- function(
  graph = NULL,
  nodes = 0,
  mode = c("all", "out", "in", "total"),
  loops
) {
  if (!lifecycle::is_present(loops)) {
    lifecycle::deprecate_warn(
      when = "2.0.0",
      what = "centr_degree_tmax(loops = 'must be explicit')",
      details = "The default value (currently `FALSE`) will be dropped in the next release. Add an explicit value for the `loops` argument."
    )
    loops <- FALSE
  }

  # Argument checks
  ensure_igraph(graph, optional = TRUE)

  nodes <- as.numeric(nodes)
  mode <- switch(
    igraph.match.arg(mode),
    "out" = 1,
    "in" = 2,
    "all" = 3,
    "total" = 3
  )
  loops <- as.logical(loops)

  on.exit(.Call(R_igraph_finalizer))
  # Function call
  res <- .Call(R_igraph_centralization_degree_tmax, graph, nodes, mode, loops)

  res
}


#' Centralize a graph according to the betweenness of vertices
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph.
#' @param directed logical scalar, whether to use directed shortest paths for
#'   calculating betweenness.
#' @param normalized Logical scalar. Whether to normalize the graph level
#'   centrality score by dividing by the theoretical maximum.
#' @return A named list with the following components:
#'   \describe{
#'     \item{res}{
#'       The node-level centrality scores.
#'     }
#'     \item{centralization}{
#'       The graph level centrality index.
#'     }
#'     \item{theoretical_max}{
#'       The maximum theoretical graph level centralization score
#'       for a graph with the given number of vertices,
#'       using the same parameters.
#'       If the `normalized` argument was `TRUE`,
#'       then the result was divided by this number.
#'     }
#'   }
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_degree(g)$centralization
#' centr_clo(g, mode = "all")$centralization
#' centr_betw(g, directed = FALSE)$centralization
#' centr_eigen(g, directed = FALSE)$centralization
centr_betw <- function(graph, directed = TRUE, normalized = TRUE) {
  # Argument checks
  ensure_igraph(graph)

  directed <- as.logical(directed)
  normalized <- as.logical(normalized)

  on.exit(.Call(R_igraph_finalizer))
  # Function call
  res <- .Call(R_igraph_centralization_betweenness, graph, directed, normalized)

  res
}

#' Theoretical maximum for betweenness centralization
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph. It can also be `NULL` if
#'   `nodes` and `directed` are both given.
#' @param nodes The number of vertices. This is ignored if the graph is
#'   given.
#' @param directed Logical scalar, whether to use directed shortest paths
#'   for calculating betweenness. Ignored if an undirected graph was
#'   given.
#' @return Real scalar, the theoretical maximum (unnormalized) graph
#'   betweenness centrality score for graphs with given order and other
#'   parameters.
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_betw(g, normalized = FALSE)$centralization %>%
#'   `/`(centr_betw_tmax(g))
#' centr_betw(g, normalized = TRUE)$centralization
#' @cdocs igraph_centralization_betweenness_tmax
centr_betw_tmax <- centralization_betweenness_tmax_impl

#' Centralize a graph according to the closeness of vertices
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph.
#' @param mode This is the same as the `mode` argument of
#'   `closeness()`.
#' @param normalized Logical scalar. Whether to normalize the graph level
#'   centrality score by dividing by the theoretical maximum.
#' @return A named list with the following components:
#'   \describe{
#'     \item{res}{
#'       The node-level centrality scores.
#'     }
#'     \item{centralization}{
#'       The graph level centrality index.
#'     }
#'     \item{theoretical_max}{
#'       The maximum theoretical graph level centralization score
#'       for a graph with the given number of vertices,
#'       using the same parameters.
#'       If the `normalized` argument was `TRUE`,
#'       then the result was divided by this number.
#'     }
#'   }
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_degree(g)$centralization
#' centr_clo(g, mode = "all")$centralization
#' centr_betw(g, directed = FALSE)$centralization
#' centr_eigen(g, directed = FALSE)$centralization
#' @cdocs igraph_centralization_closeness
centr_clo <- centralization_closeness_impl

#' Theoretical maximum for closeness centralization
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph. It can also be `NULL` if
#'   `nodes` is given.
#' @param nodes The number of vertices. This is ignored if the graph is
#'   given.
#' @param mode This is the same as the `mode` argument of
#'   `closeness()`. Ignored if an undirected graph is given.
#' @return Real scalar, the theoretical maximum (unnormalized) graph
#'   closeness centrality score for graphs with given order and other
#'   parameters.
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_clo(g, normalized = FALSE)$centralization %>%
#'   `/`(centr_clo_tmax(g))
#' centr_clo(g, normalized = TRUE)$centralization
#' @cdocs igraph_centralization_closeness_tmax
centr_clo_tmax <- centralization_closeness_tmax_impl

#' Centralize a graph according to the eigenvector centrality of vertices
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph.
#' @param directed logical scalar, whether to use directed shortest paths for
#'   calculating eigenvector centrality.
#' @param scale `r lifecycle::badge("deprecated")` Ignored. Computing
#' eigenvector centralization requires normalized eigenvector centrality scores.
#' @param options This is passed to [eigen_centrality()], the options
#'   for the ARPACK eigensolver.
#' @param normalized Logical scalar. Whether to normalize the graph level
#'   centrality score by dividing by the theoretical maximum.
#' @return A named list with the following components:
#'   \describe{
#'     \item{vector}{
#'       The node-level centrality scores.
#'     }
#'     \item{value}{
#'       The corresponding eigenvalue.
#'     }
#'     \item{options}{
#'       ARPACK options, see the return value of [eigen_centrality()] for details.
#'     }
#'     \item{centralization}{
#'       The graph level centrality index.
#'     }
#'     \item{theoretical_max}{
#'       The same as above, the theoretical maximum centralization score
#'       for a graph with the same number of vertices.
#'     }
#'   }
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_degree(g)$centralization
#' centr_clo(g, mode = "all")$centralization
#' centr_betw(g, directed = FALSE)$centralization
#' centr_eigen(g, directed = FALSE)$centralization
#'
#' # The most centralized graph according to eigenvector centrality
#' g0 <- make_graph(c(2, 1), n = 10, dir = FALSE)
#' g1 <- make_star(10, mode = "undirected")
#' centr_eigen(g0)$centralization
#' centr_eigen(g1)$centralization
#' @cdocs igraph_centralization_eigenvector_centrality
centr_eigen <- function(
  graph,
  directed = FALSE,
  scale = deprecated(),
  options = arpack_defaults(),
  normalized = TRUE
) {
  if (lifecycle::is_present(scale)) {
    lifecycle::deprecate_soft(
      "2.2.0",
      "centr_eigen(scale = )",
      details = "The function always behaves as if `scale = TRUE`.
      The argument will be removed in the future."
    )
  }

  centralization_eigenvector_centrality_impl(
    graph = graph,
    directed = directed,
    options = options,
    normalized = normalized,
    scale = TRUE
  )
}

#' Theoretical maximum for eigenvector centralization
#'
#' See [centralize()] for a summary of graph centralization.
#'
#' @param graph The input graph. It can also be `NULL`, if
#'   `nodes` is given.
#' @param nodes The number of vertices. This is ignored if the graph is
#'   given.
#' @param directed logical scalar, whether to consider edge directions
#'   during the calculation. Ignored in undirected graphs.
#' @param scale `r lifecycle::badge("deprecated")` Ignored. Computing
#' eigenvector centralization requires normalized eigenvector centrality scores.
#' @return Real scalar, the theoretical maximum (unnormalized) graph
#'   eigenvector centrality score for graphs with given vertex count and
#'   other parameters.
#'
#' @family centralization related
#'
#' @export
#'
#' @examples
#' # A BA graph is quite centralized
#' g <- sample_pa(1000, m = 4)
#' centr_eigen(g, normalized = FALSE)$centralization %>%
#'   `/`(centr_eigen_tmax(g))
#' centr_eigen(g, normalized = TRUE)$centralization
#' @cdocs igraph_centralization_eigenvector_centrality_tmax
centr_eigen_tmax <- function(
  graph = NULL,
  nodes = 0,
  directed = FALSE,
  scale = deprecated()
) {
  if (lifecycle::is_present(scale)) {
    lifecycle::deprecate_soft(
      "2.2.0",
      "centr_eigen_tmax(scale = )",
      details = "The function always behaves as if `scale = TRUE`.
      The argument will be removed in the future."
    )
  }

  centralization_eigenvector_centrality_tmax_impl(
    graph = graph,
    nodes = nodes,
    directed = directed,
    scale = TRUE
  )
}