HITS Algorithm Calculation Example

The equations for HITS algorithm are:

a = L'h (L' denoting transpose of adjacency matrix L)
h = La

a, h denoting the authority score and hub score respectively.

The following python code shall compute the hub score and authority score for this particular graph:

import numpy as np

adjacency_mtx = np.matrix([

  [0, 0, 0, 1, 0],
  [0, 0, 0, 1, 1],
  [0, 0, 0, 1, 0],
  [0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0]
 ])
hub_score = np.matrix([ #initial guess
  [2],
  [2],
  [2],
  [2],
  [2]
 ])
authority_score = np.matrix.transpose(adjacency_mtx)*hub_score
hub_score = adjacency_mtx*authority_score

print authority_score
print hub_score

#output:
[[0]
 [0]
 [0]
 [6]
 [2]]

[[6]
 [8]
 [6]
 [0]
 [0]]

This matches our intuition that, node 4 has a higher authority over node 5 and node 2 is a better hub than nodes 1 and 3.