R/spectral.gap.R

In netrankr: Analyzing Partial Rankings in Networks

#' @title Spectral gap of a graph
#' @description  The spectral (or eigen) gap of a graph is the absolute
#'  difference between the biggest and second biggest eigenvalue
#' of the adjacency matrix. To compare spectral gaps across networks, the fraction can be used.
#'
#' @param g igraph object
#' @param method A string, either "frac" or "abs"
#' @return Numeric value
#' @details The spectral gap is bounded between 0 and 1 if `method="frac"`. The closer
#' the value to one, the bigger the gap.
#' @author David Schoch
#' @examples
#' # The fractional spectral gap of a threshold graph is usually close to 1
#' g <- threshold_graph(50, 0.3)
#' spectral_gap(g, method = "frac")
#' @export
#'
spectral_gap <- function(g, method = "frac") {
  spec_decomp <- eigen(igraph::get.adjacency(g, "both"))$values[c(1, 2)]
  if (method == "frac") {
    return(1 - spec_decomp[2] / spec_decomp[1])
  } else if (method == "abs") {
    return(spec_decomp[1] - spec_decomp[2])
  } else {
    stop("method must be one of 'frac' or 'abs'")
  }
}