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#' Similarity measures of two vertices
#'
#' These functions calculates similarity scores for vertices based on their
#' connection patterns.
#'
#' @details
#' The Jaccard similarity coefficient of two vertices is the number of common
#' neighbors divided by the number of vertices that are neighbors of at least
#' one of the two vertices being considered. The \code{jaccard} method
#' calculates the pairwise Jaccard similarities for some (or all) of the
#' vertices.
#'
#' The Dice similarity coefficient of two vertices is twice the number of
#' common neighbors divided by the sum of the degrees of the vertices.
#' Methof \code{dice} calculates the pairwise Dice similarities for some
#' (or all) of the vertices.
#'
#' The inverse log-weighted similarity of two vertices is the number of their
#' common neighbors, weighted by the inverse logarithm of their degrees. It is
#' based on the assumption that two vertices should be considered more similar
#' if they share a low-degree common neighbor, since high-degree common
#' neighbors are more likely to appear even by pure chance. Isolated vertices
#' will have zero similarity to any other vertex. Self-similarities are not
#' calculated. See the following paper for more details: Lada A. Adamic and
#' Eytan Adar: Friends and neighbors on the Web. Social Networks,
#' 25(3):211-230, 2003.
#'
#' @aliases similarity.jaccard similarity.dice similarity.invlogweighted
#' @param graph The input graph.
#' @param vids The vertex ids for which the similarity is calculated.
#' @param mode The type of neighboring vertices to use for the calculation,
#' possible values: \sQuote{\code{out}}, \sQuote{\code{in}},
#' \sQuote{\code{all}}.
#' @param loops Whether to include vertices themselves in the neighbor
#' sets.
#' @param method The method to use.
#' @return A \code{length(vids)} by \code{length(vids)} numeric matrix
#' containing the similarity scores. This argument is ignored by the
#' \code{invlogweighted} method.
#' @author Tamas Nepusz \email{ntamas@@gmail.com} and Gabor Csardi
#' \email{csardi.gabor@@gmail.com} for the manual page.
#' @seealso \code{\link{cocitation}} and \code{\link{bibcoupling}}
#' @references Lada A. Adamic and Eytan Adar: Friends and neighbors on the Web.
#' \emph{Social Networks}, 25(3):211-230, 2003.
#' @keywords graphs
#' @export
#' @examples
#'
#' g <- make_ring(5)
#' similarity(g, method = "dice")
#' similarity(g, method = "jaccard")
similarity <- function(graph, vids = V(graph), mode = c("all", "out", "in",
"total"), loops = FALSE, method = c("jaccard",
"dice", "invlogweighted")) {
method <- igraph.match.arg(method)
if (method == "jaccard") {
similarity.jaccard(graph, vids, mode, loops)
} else if (method == "dice") {
similarity.dice(graph, vids, mode, loops)
} else if (method == "invlogweighted") {
similarity.invlogweighted(graph, vids, mode)
}
}
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