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