#library
library(igraph)
library(sand)
library(igraphdata) 
library(sna)
library(network)
library(statnet)
library(intergraph)
####upload the data
data(aidsblog)
?aidsblog
data(yeast)
?yeast
#let's explore the data
?yeast
?aidsblog
#first visualization 
plot(yeast, vertex.label=NA, vertex.size=3, layout=layout_with_kk, edge.arrow.size=0.2)
plot(aidsblog, vertex.label=NA, vertex.size=3, layout=layout_with_kk,edge.arrow.size=0.2)
#Let's start!! 

#According to the nature of the data:
#1) compute and comment some global network statistics 
#(including size, number of edges, and diameter, please refer 
#for instance to the example of co-authorship in the data collection slides)
#network exploration:
E(yeast) # The edges of the object
V(yeast) # The verteces of the object
yeast[]#to visualize the matrix
class(yeast)
#it is possibile to convert the igraph object into a network.
#Ofc it is possible to work also without converting
?asNetwork
net_yeast<-asNetwork(yeast)###using the library intergraph we can convert the igraph obj into a network
net_aids <- asNetwork(aidsblog) #secondo network
gplot(net_yeast)
?gplot#visualization using the library sna
igraph::ecount(yeast) #number of edges
gsize(yeast) # same result of ecount. Infact ecount() and gsize() are aliases
vcount(yeast) #number of vertices
gorder(yeast) #vcount() and gorder() are aliases.

#let's see some other functions:
igraph::edge_density(yeast, loops=F) #The proportion of present edges from all possible edges in the network.
sna::gden(net_yeast, mode="graph")
?gden# Density

network::network.size(net_yeast) #network size returns the number of vertices
length(yeast) #returns the number of vertices

sna::isolates(net_yeast) #returns a list of the isolated nodes

#let's see the degree
deg_yeast <- igraph::degree(yeast) #the number of its adjacent edges.
sna::degree(net_yeast)
max(deg_yeast)
min(deg_yeast)
mean(igraph::degree(yeast))
#other way to find isolates node
which(igraph::degree(yeast)==0)
table(deg_yeast)
plot(yeast, vertex.size=deg_yeast/5, layout=layout_with_kk, vertex.label=NA,edge.arrow.size=0.5)
#we don't have any node with degree 0

igraph::diameter(yeast, directed=F) #diameter: The diameter of a graph is the length of the longest geodesic.

igraph::reciprocity(yeast) #######The reciprocity of directed network reflects the proportion of edges that are symmetrical.
igraph::reciprocity(aidsblog)

aids_simply <- simplify(aidsblog, remove.multiple = F, remove.loops = T) 
plot(aids_simply, vertex.label=NA, vertex.size=3, layout=layout_with_kk,edge.arrow.size=0.2)

?transitivity
igraph::transitivity(yeast) #Transitivity measures the probability that the adjacent vertices of a vertex are connected. 
#This is sometimes also called the clustering coefficient.
sna::gtrans(net_yeast[,]) 

sna::betweenness(net_yeast, gmode="graph") # betweenness
igraph::betweenness(yeast)
?betweenness

igraph::closeness(yeast) #closeness

?centr_clo
centr <- igraph::centr_clo(yeast, mode="all", normalized=T) #centralize according to the 
centr$centralization #The graph level centrality index.Concentration of edges


hist(igraph::degree(yeast), col="blue",breaks=50, xlim=c(0, 50), xlab="Vertex Degree", ylab="Frequency", main="") #degree
hist(igraph::degree(yeast))
average.path.length(yeast)
diameter(yeast)

####second network

?degree
deg_all <- igraph::degree(aidsblog, mode="all") # Default: total degree
ideg <- igraph::degree(aidsblog, mode="out") 
odeg <- igraph::degree(aidsblog, mode="in")

deg_all2 <- sna::degree(net_yeast, gmode="graph") # Default: total degree
ideg2 <- sna::degree(net_yeast, cmode="indegree") 
odeg3 <- sna::degree(net_yeast, cmode="outdegree")

diameter(aidsblog, directed=T) #diameter


#2) if needed decompose the network into distinct components
#Component subgraphs (or simply components) are portions of the network that are disconnected from each other.
V(yeast)$name


#3) compute some centrality scores for the individual vertices
#ev <- sna::evcent(net_yeast) # eigenvector centrality
#ev 



#evdf <- data.frame(net_yeast %v% "name",ev) 
#evdf

#evdf[order(evdf$ev, decreasing = TRUE), c(1,2)]

?centralization
centralization(net_yeast, degree) # Concentration of edges
centralization(net_yeast, sna::betweenness)

sna::dyad.census(net_yeast)
#sna::triad.census(net_yeast)
#triad.census(netgot, mode="graph") 

tc<-sna::triad.census(netgot) # directed triad census
barplot(tc, names.arg=colnames(tc), las=2)

barplot(tc[-1]/sum(triad.census(netgot)[-1]), names.arg=colnames(tc)[-1], las=2)

edge_density(yeast)


#####
comp_y <- sna::components(net_yeast)# Strong component count
comp_a <- sna::components(net_aids)

comp_y2 <- components(net_yeast, connected="weak") # Weak component count
comp_a2 <- components(net_aids, connected="weak") # Weak component count
##get the largest component 
cl_y <- component.largest(net_yeast, connected="weak")
cl_y

cl_y2 <- component.largest(net_yeast)
cl_y2
#plot
gplot(net_yeast[cl_y,cl_y], boxed.lab=FALSE, label.cex=0.5,label.col=4,label=network.vertex.names(net_yeast)[cl_y])

?decompose

comps_y <- decompose.graph(yeast)
table(sapply(comps_y, vcount))

yeast.gc <- decompose.graph(yeast)[[1]]
plot(yeast.gc, vertex.label="", vertex.size=5)

#4) extract the ego-network the most central vertex according to at least 2 centrality score (e.g., degree and closeness) and compute and comment the local clustering coefficient 
select <- which(V(yeast)==max(deg_yeast))
nodes_of_interest <- c("YDL136W")
#V(yeast)$name
#selnodes <- V(yeast)[name %in% nodes_of_interest]
#selegoV <- ego(yeast, order=1, nodes = selnodes, mode = "all", mindist = 0)
#plot(selegoV[[2]], vertex.label=NA)
#class(selegoV)
# turn the returned list of igraph.vs objects into a graph
#selegoG <- induced_subgraph(yeast,unlist(selegoV))

# plot the subgraph
plot(selegoG, vertex.size=5, vertex.label=NA, edge.size=0.2)
ego.instr_y <- induced_subgraph(yeast, degree) 
ego.instr <- induced_subgraph(yeast, igraph::neighborhood(yeast, order= 1, n= "YDL136W" )[[1]])