Nonderogatory Directed Webgraph

Algorithm 1

Input: 𝑚, 𝑛 and 𝑀=𝑥𝐼−𝐴(𝑊(𝑚,𝑛))

(1) for  𝑘=0→𝑚𝑛−𝑚  by  𝑚  do

(2)  for  𝑖=𝑚→2  by  (−1)  do

(3)     𝑐_{𝑘+𝑖−1}←𝑥×𝑐_𝑘+𝑖+𝑐_{𝑘+𝑖−1}

(4)  end for

(5)  for  𝑖=1→𝑚−1  do

(6)     𝑟_𝑘+𝑚←𝑀_{𝑘+𝑚,𝑘+𝑖+1}×𝑟_𝑘+𝑖+𝑟_𝑘+𝑚

(7)  end for

(8)  if  (𝑘<𝑚𝑛−𝑚)  then

(9)   for  𝑖=𝑘+2→𝑘+𝑚  do

(10)    𝑐_{𝑖+𝑚−1}←(−1)×𝑐_𝑖+𝑐_{𝑖+𝑚−1}

(11)        end for

(12)  end if

(13)  for  𝑖=1→𝑚−1  do

(14)      𝑐_𝑘+𝑖↔𝑐_𝑘+𝑖+1

(15)  end for

(16) end for

(17) for  𝑘=𝑚𝑛−𝑚→𝑚  by  (−𝑚)  do

(18)  for  𝑖=𝑚𝑛−1→𝑚+1  by  (−1)  do

(19)     if  (𝑖mod𝑚≠0)  then

(20)    𝑟_𝑘←𝑀_𝑘𝑖×𝑟_𝑖+𝑟_𝑘

(21)     end if

(22)  end for

(23) end for

Output: 𝑀