setwd('/Users/ovitek/Dropbox/Olga/Teaching/CS6220/Fall15/LectureNotes/8-graphs')
library(igraph)

# Generate a random graph
# p.96 of the notes
# 20 vertices. prob(edge between two nodes)
# g <- random.graph.game(20,5/20, directed=TRUE) # depreciated
g <- sample_gnp(20,5/20, directed=TRUE) # Graph(node,probability)

# another possible way to simulate graphs
# g <- sample_gnm(20,40, directed=TRUE) # Graph(node,edge)

plot(g)
page.rank(g)

# Generate a graph structure from an adjecency matrix
# p.104 of the notes
A <- matrix(c(
	0,1,1,0,0,0,
	1,0,1,1,1,1,
	0,1,0,0,0,0,
	0,0,1,0,1,0,
	0,1,1,0,0,0,
	0,0,1,0,0,0
), nrow=6, ncol=6, byrow=TRUE)
vertexLabels <- c('Wikipedia', 'Google', 'Bing', 'Yahoo', 'Altavista', 'Rediffmail')
dimnames(A)[[2]] <- vertexLabels
G <- graph.adjacency(A, mode=c('directed'), weighted=NULL)
plot(G)

# Graph properties
#-------------------
degree(G)
shortest.paths(G)
betweenness(G)
page.rank(G)$vector

# A preview of the HITS algorithm
#-----------------------------------
a1 <- t(A) %*% rep(1, 6)
a1 <- a1/sqrt(sum(a1^2))
h1 <- A %*% a1
h1 <- h1/sqrt(sum(h1^2))
a2 <- t(A) %*% a1
a2 <- a2/sqrt(sum(a2^2))

# A preview of neighborhood-based methods
#--------------------------------------------
V(G)  # list of vertices
V(G)['Yahoo'] # select the 'Yahoo' vertice 
V(G)[nei(V(G)['Yahoo'])] #'nei' is only used while subsetting