An Adaptive Reordered Method for Computing PageRank

Algorithm 2

The adaptive reordered algorithm.

(1) Reorder the hyperlink matrix so that in the top left submatrix all the zero rows

  are at the bottom in every reordering procedure, until the given stopping criterion

  is reached.

(2) Solve 𝐱^𝑇₁(𝐈−𝛼𝐏₁₁)=𝐯^𝑇₁ using Jacobi method.

(3) For 𝑖=2 to 𝑏, Compute 𝐱^𝑇_𝑖=𝛼∑^𝑖−1_𝑗=1𝐱^𝑇_𝑗𝐏_𝑗𝑖+𝐯^𝑇_𝑖.

(4) Compute 𝝅^𝑇=𝐱^𝑇₁𝐱^𝑇₂⋯𝐱^𝑇_𝑏/𝐱^𝑇₁𝐱^𝑇₂⋯𝐱^𝑇_𝑏1.