bibliometrix: Comprehensive Science Mapping Analysis

Documented in networkStat

#' Calculating network summary statistics
#'
#' \code{networkStat} calculates main network statistics.
#'
#' The function \code{\link{networkStat}} can calculate the main network statistics from a bibliographic network previously created by \code{\link{biblioNetwork}}.
#' @param object is a network matrix obtained by the function \code{\link{biblioNetwork}} or an graph object of the class \code{igraph}.
#' @param stat is a character. It indicates which statistics are to be calculated. \code{stat = "network"} calculates the statistics related to the network;
#' \code{stat = "all"} calculates the statistics related to the network and the individual nodes that compose it. Default value is \code{stat = "network"}.
#' @param type is a character. It indicates which centrality index is calculated. type values can be c("degree", "closeness", "betweenness","eigenvector","pagerank","hub","authority", "all"). Default is "degree".
#' @return It is a list containing the following elements:
#' \tabular{lll}{
#' \code{graph} \tab  \tab a network object of the class \code{igraph}\cr
#' \code{network} \tab  \tab a \code{communities} a list with the main statistics of the network\cr
#' \code{vertex} \tab  \tab a data frame with the main measures of centrality and prestige of vertices.\cr}
#'
#'
#' @examples
#' # EXAMPLE Co-citation network
#'
#' # to run the example, please remove # from the beginning of the following lines
#' # data(scientometrics, package = "bibliometrixData")
#'
#' # NetMatrix <- biblioNetwork(scientometrics, analysis = "co-citation",
#' #      network = "references", sep = ";")
#'
#' # netstat <- networkStat(NetMatrix, stat = "all", type = "degree")
#'
#' @seealso \code{\link{biblioNetwork}} to compute a bibliographic network.
#' @seealso \code{\link{cocMatrix}} to compute a co-occurrence matrix.
#' @seealso \code{\link{biblioAnalysis}} to perform a bibliometric analysis.
#'
#' @export
networkStat <- function(object, stat = "network", type = "degree") {
  if (!inherits(object, "igraph")) {
    # Create igraph object
    net <- graph.adjacency(object, mode = "undirected", weighted = NULL)
    V(net)$id <- colnames(object)
  } else {
    net <- object
    V(net)$id <- V(net)$name
  }

  net <- simplify(net, remove.loops = T)

  ### network statistics
  networkSize <- vcount(net)

  # The proportion of present edges from all possible edges in the network.
  networkDensity <- edge_density(net, loops = FALSE)

  # Transitivity
  # global - ratio of triangles (direction disregarded) to connected triples.
  TR <- transitivity(net, type = "global")
  # local - ratio of triangles to connected triples each vertex is part of.
  # TRL=transitivity(net, type="local")

  # Diameter
  # A network diameter is the longest geodesic distance
  # (length of the shortest path between two nodes) in the network
  DIAM <- diameter(net, directed = F, weights = NA)

  # Degree distribution
  deg <- degree(net, mode = "all")
  deg.dist <- degree_distribution(net, cumulative = T, mode = "all")

  # plot( x=0:max(deg), y=1-deg.dist, pch=19, cex=1.2, col="orange",
  #      xlab="Degree", ylab="Cumulative Frequency")


  # Network centralization
  # Degree (number of ties)degree
  NCD <- NCC <- NCB <- NCE <- pagerank <- hub <- authority <- NA
  switch(type,
    degree = {
      NCD <- centr_degree(net, mode = "all", normalized = T)$centralization
    },
    closeness = { # Closeness (centrality based on distance to others in the graph)
      NCC <- suppressWarnings(centr_clo(net, mode = "all", normalized = T)$centralization)
    },
    betweenness = { # Betweenness (centrality based on a broker position connecting others)
      NCB <- centr_betw(net, directed = F, normalized = T)$centralization
    },
    eigenvector = { # Eigenvector (centrality proportional to the sum of connection centralities)
      NCE <- centr_eigen(net, directed = F, normalized = T)$centralization
    },
    pagerank = {
      NCD <- centr_degree(net, mode = "all", normalized = T)$centralization
    },
    hub = {
      NCD <- centr_degree(net, mode = "all", normalized = T)$centralization
    },
    authority = {
      NCD <- centr_degree(net, mode = "all", normalized = T)$centralization
    }
  )
  # Average path length
  # the mean of the shortest distance between each pair of nodes in the network (in both directions for directed graphs).
  meanDistance <- mean_distance(net, directed = F)

  networkResults <- list(
    networkSize = networkSize,
    networkDensity = networkDensity,
    networkTransitivity = TR,
    networkDiameter = DIAM,
    networkDegreeDist = deg.dist,
    networkCentrDegree = NCD,
    networkCentrCloseness = NCC,
    networkCentrEigen = NCE,
    networkCentrbetweenness = NCB,
    NetworkAverPathLeng = meanDistance
  )

  ### Centrality and Prestige of vertices
  if (stat == "all") {
    DC <- CC <- BC <- EC <- PR <- HS <- AS <- NA

    switch(type,
      degree = {
        # Degree centrality.
        # The simplest way to quantify a node'simportance is to consider the number of nodes it is incident with,
        # with high numbers interpreted to be of higher importance.
        # standardized index is: Ei/(N-1)
        DC <- degree(net, v = V(net), mode = c("all"), loops = TRUE, normalized = TRUE)
      },
      closeness = {
        # Closeness centrality.
        # Nodes can also be indexed by con-sidering their geodesic distance to each other.
        CC <- suppressWarnings(closeness(net, vids = V(net), mode = c("all"), normalized = TRUE))
      },
      betweenness = {
        # Betweenness centrality.
        # Another way to gauge a node's influence is to consider its role in linking other nodes together in the network.
        BC <- betweenness(net, v = V(net), directed = FALSE, weights = NULL, normalized = TRUE)
      },
      eigenvector = {
        # Eigenvector centrality.
        # Eigenvector centrality is another measure of centrality.
        # The eigenvector centrality ofeach node can be found by computing the leading
        EC <- eigen_centrality(net, directed = FALSE, scale = TRUE, weights = NULL, options = arpack_defaults)$vector
      },
      pagerank = {
        # PageRank ranking of vertices
        PR <- page_rank(net,
          algo = c("prpack"), vids = V(net),
          directed = FALSE, damping = 0.85, personalized = NULL, weights = NULL,
          options = NULL
        )$vector
      },
      hub = {
        ### Hubs and authorities
        # The hubs and authorities algorithm developed by Jon Kleinberg was initially used to examine web pages.
        # Hubs were expected to contain catalogs with a large number of outgoing links; while authorities would get
        # many incoming links from hubs, presumably because of their high-quality relevant information.

        # Hubs
        HS <- hub_score(net, weights = NA)$vector
      },
      authority = {
        # Authorities
        AS <- authority_score(net, weights = NA)$vector
      },
      all = {
        DC <- degree(net, v = V(net), mode = c("all"), loops = TRUE, normalized = TRUE)
        CC <- suppressWarnings(closeness(net, vids = V(net), mode = c("all"), normalized = TRUE))
        BC <- betweenness(net, v = V(net), directed = FALSE, weights = NULL, normalized = TRUE)
        EC <- eigen_centrality(net, directed = FALSE, scale = TRUE, weights = NULL, options = arpack_defaults)$vector
        PR <- page_rank(net,
          algo = c("prpack"), vids = V(net),
          directed = FALSE, damping = 0.85, personalized = NULL, weights = NULL,
          options = NULL
        )$vector
        HS <- hub_score(net, weights = NA)$vector
        AS <- authority_score(net, weights = NA)$vector
      }
    )

    vertexResults <- data.frame(
      vertexID = V(net)$id,
      vertexCentrDegree = DC,
      vertexCentrCloseness = CC,
      vertexCentrEigen = EC,
      vertexCentrBetweenness = BC,
      vertexPageRank = PR,
      vertexHub = HS,
      vertexAuthority = AS
    )

    # res=PCA(vertexResults[,-1],graph=FALSE)

    # R=rank(-res$ind$coord[,1]-min(res$ind$coord[,1]))

    # vertexResults$Ranking=R
  } else {
    vertexResults <- NA
  }
  netstat <- list(graph = net, network = networkResults, vertex = vertexResults, stat = stat, type = type)
  class(netstat) <- "bibliometrix_netstat"
  return(netstat)
}