# HITS.R  (Mauro Brunato, april 2007)
#
# Computing HITS authority and hub scores.
# 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();

#####################################
#
# HITS SCORE COMPUTATION
#

# Initialize scores uniformly
#
authority <- matrix ( rep (1, N), N );
hub <- matrix ( rep (1, N), N );

# Uncomment to show initial scores and stop
#
#matrix(c(hub, authority), N);q();

# Compute the two transition matrices
#
E <- graph;
tE <- t(E);

# Iterate through the HITS algorithm
#
for ( i in 1:101 ) {
	oldauthority <- authority;
	authority <- tE %*% hub;
	hub <- E %*% oldauthority;
	authority <- authority / sum(authority);
	hub <- hub / sum(hub);
}

# Print the final scores
#
print (matrix(c(hub, authority), N));