R/degree.R

In rhype: Work with Hypergraphs in R

#' Find the Degree of Vertices in a Hypergraph
#'
#' The degree of a vertex is a way of expressing how many connections there
#' are from a vertex to the rest of the hypergraph. The current version of
#' rhype has three methods for computing degree.
#'
#' `"vertex"` counts the number of ways it is possible to move to another
#' vertex. If there are multiple hyperedges connecting two vertices, then each
#' of these hyperedges will be counted as a new way to move between these two
#' vertices. For weighted hypergraphs or hypergraphs with real coefficients,
#' the strength of connection between two vertices is a functions of the weights
#' and real coefficients.
#'
#' `"vertex_simple"` just counts the number of vertices it is possible to reach
#' in one step from the given vertex, no matter how many hyperedges connect them.
#'
#' `"hyperedge"` represents the strength with which a vertex connects with
#' itself through the hyperedges it is a member of. This is taken from the work
#' of Jurgen Jost and Raffaella Mulas \doi{10.1016/j.aim.2019.05.025}. For
#' unweighted hypergraphs without real coefficients this is equivalent to
#' `"hyperedge_simple"`.
#'
#' `"hyperedge_simple"` just counts the number of hyperedges a vertex is a
#' member of.
#'
#' @param hype A hypergraph object
#' @param method The method for calculating degree. Out of `"vertex"`,
#' `"vertex_simple"`, `"hyperedge"` and `"hyperedge_simple"`
#'
#' @return A vector representing the degree of each vertex with respect to the
#' given method.
#' @export
#'
#' @examples
#' h1 <- example_hype()
#' degree(h1)
degree <- function(hype, method = "vertex") {
  # Checking the hyeprgraph is not oriented
  if (hype$get_oriented()) {
    stop("\n \u2716 Degree not yet supported for oriented hypergraphs")
  }

  # Checking method and computing the corresponding degree
  if (method == "vertex") {
    # Finding the adjacency matrix
    adj_mat <- adjacency_matrix(hype, normalise = FALSE, self_adj = FALSE)
    # Row summing the adjacency matrix
    return(
      apply(adj_mat, 1, sum)
    )
  } else if (method == "vertex_simple") {
    # Finding the normalised adjacency matrix
    adj_mat <- adjacency_matrix(hype, normalise = TRUE, self_adj = FALSE)
    # Row summing the normalised adjacency matrix
    return(apply(adj_mat, 1, sum))
  } else if (method == "hyperedge") {
    # Finding the adjacency matrix with self adjacency
    adj_mat <- adjacency_matrix(hype, normalise = FALSE, self_adj = TRUE)
    # Returning the self adjacency
    return(Matrix::diag(adj_mat))
  } else if (method == "hyperedge_simple") {
    # Finding the incidence matrix
    inc_mat <- incidence_matrix(hype)
    # Normalising the incidence matrix
    inc_mat <- matrix(as.numeric(inc_mat != 0), nrow = dim(inc_mat)[1])
    # Row summing the incidence matrix and returning this value
    return(apply(inc_mat, 1, sum))
  }
}