```
#' 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"). 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{\link{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)
#'
#' # 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 (class(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, nobigint = TRUE, 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
}
)
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)
}
```

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