"""PageRank algorithm with explicit number of iterations.
Returns
-------
ranking of nodes (pages) in the adjacency matrix
"""
import numpy as np
def pagerank(M, num_iterations: int = 100, d: float = 0.85):
"""PageRank: The trillion dollar algorithm.
Parameters
----------
M : numpy array
adjacency matrix where M_i,j represents the link from 'j' to 'i', such that for all 'j'
sum(i, M_i,j) = 1
num_iterations : int, optional
number of iterations, by default 100
d : float, optional
damping factor, by default 0.85
Returns
-------
numpy array
a vector of ranks such that v_i is the i-th rank from [0, 1],
v sums to 1
"""
N = M.shape[1]
v = np.random.rand(N, 1)
v = v / np.linalg.norm(v, 1)
M_hat = (d * M + (1 - d) / N)
for i in range(num_iterations):
v = M_hat @ v
return v
M = np.array([[0, 0, 0, 0, 1],
[0.5, 0, 0, 0, 0],
[0.5, 0, 0, 0, 0],
[0, 1, 0.5, 0, 0],
[0, 0, 0.5, 1, 0]])
v = pagerank(M, 100, 0.85)