1.  encodings

2. 

findPi <- function(adj,k) {
   # find the numbers of outlinks
   ni <- apply(adj,1,sum)
   # construct transition matrix
   n <- nrow(adj)
   p <- matrix(0.0,nrow=n,ncol=n)
   for (i in 1:n) {
      recip <- 1/ni[i]
      outlinks <- which(adj[i,] == 1)
      p[i,outlinks] <- recip
   }
   if (k > 0) {
      # form powers
      m <- p
      for (i in 1:ceiling(log2(k))) {
         m <- m %*% m
      }
      # for better accuracy, average the n estimates of pi
      colMeans(m)
   } else {
      vec <- eigen(t(p))$vectors[,1]
      vec <- Re(vec)
      vec / sum(vec)
   }
}

print(findPi(rbind(c(0,1,0),c(1,0,1),c(1,0,0)),k=10))
print(findPi(rbind(c(0,1,0),c(1,0,1),c(1,0,0)),k=0))