页面排名算法和使用Python的实现

PageRank算法适用于网页。网页是有向图，我们知道有向图的两个组成部分是节点和连接。页面是节点，超链接是连接，即两个节点之间的连接。

我们可以通过PageRank找出每个页面的重要性，并且它是准确的。PageRank的值是概率在0到1之间。

图中单个节点的PageRank值取决于与其连接的所有节点的PageRank值，并且这些节点周期性地连接至我们想要对其排名的节点，我们使用收敛迭代方法将值分配给PageRank。

范例程式码

import numpy as np
import scipy as sc
import pandas as pd
from fractions import Fraction
   def display_format(my_vector, my_decimal):
      return np.round((my_vector).astype(np.float), decimals=my_decimal)
      my_dp = Fraction(1,3)
      Mat = np.matrix([[0,0,1],
      [Fraction(1,2),0,0],
      [Fraction(1,2),1,0]])
      Ex = np.zeros((3,3))
      Ex[:] = my_dp
      beta = 0.7
      Al = beta * Mat + ((1-beta) * Ex)
      r = np.matrix([my_dp, my_dp, my_dp])
      r = np.transpose(r)
      previous_r = r
   for i in range(1,100):
      r = Al * r
      print (display_format(r,3))
if (previous_r==r).all():
   break
previous_r = r
print ("Final:\n", display_format(r,3))
print ("sum", np.sum(r))

输出结果

[[0.333]
[0.217]
[0.45 ]]
[[0.415]
[0.217]
[0.368]]
[[0.358]
[0.245]
[0.397]]
[[0.378]
[0.225]
[0.397]]
[[0.378]
[0.232]
[0.39 ]]
[[0.373]
[0.232]
[0.395]]
[[0.376]
[0.231]
[0.393]]
[[0.375]
[0.232]
[0.393]]
[[0.375]
[0.231]
[0.394]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
[[0.375]
[0.231]
[0.393]]
Final:
[[0.375]
[0.231]
[0.393]]
sum 0.9999999999999951