# PageRank.R  (Mauro Brunato, april 2007)
#
# Computing PageRank score
# Uncomment a line ending by "q()" to stop the program at that point
# and show the corresponding quantity.

##################################
#
# GRAPH DEFINITION

# The graph matrix
#
graph <- rbind (
	c( 0, 1, 0, 0, 0 ),
	c( 0, 0, 1, 0, 0 ),
	c( 1, 0, 0, 1, 0 ),
	c( 0, 1, 0, 0, 1 ),
	c( 0, 0, 0, 1, 0 ));

# Graph size
#
N <- length (graph[,1]);

# Uncomment to see the graph matrix
#
#graph;q();

#####################################
#
# PAGERANK SCORE COMPUTATION
#

# Uncomment one of the following
# the second introduces a damping factor
#
L <- graph;
#L <- graph + .01;

# Row normalization
for ( i in 1:N )
	L[i,] <- L[i,] / sum(L[i,]);

# Uncomment the following to see the transition matrix
#
#L;q();

# Set initial conditions
# Uncomment one of the following
#
rank <- matrix ( c(1, rep (0, N-1)), N );
#rank <- matrix ( rep (1, N), N );

# Uncomment to see initial ranking vector and stop
#
#rank;q();

# Compute the transpose matrix
#
tL = t(L);

# Uncomment to see the spectral decomposition and halt
#
#eigen(tL);q();

# Apply the PageRank iterations
#
for ( i in 1:101 ) {
	rank <- tL %*% rank;
	rank <- rank / sum(rank);
}

# Print the final ranking and stop
#
rank;