Python

Calculate PageRank.

Create a dictionary that contains an inverted index from the values contained in the following Text file. Assume the number in the first column is linking to the second:

1 2 1 3

2) Using this inverted index of links, create a function that calculates a vector (which you could save as a dictionary, with node numbers as keys and rank weights as values):

a) initially, all nodes should have the same weight: 1/n, where n is the number of nodes.

b) Code one cycle of rank value updates, using a value for p (the probability that a user will go directly to a node rather than following a link to it) of 0.2.

c) Once you have one cycle of rank updates working, alter your function so that it calls itself, feeding the output of one cycle into the next cycle as input, until the rank vector of a cycle is the same as the ranks from the previous cycle. Build in a trace so you can track the number of cycles. How many did it take?

d) Adjust the value of p to 0.05, and run again. Does the number of cycles change?

Text file:

0 3

0 2

0 4

0 5

3 0

3 7

3 8

3 9

3 10

3 11

3 13

3 14

3 15

3 16

3 17

3 18

3 4

3 5

2 0

2 19

2 10

2 11

2 12

2 20

2 21

2 22

2 23

2 4

2 5

4 0

4 3

4 24

4 25

4 21

4 26

4 17

4 5

5 0

5 3

5 27

5 28

5 29

5 12

5 4

1 30

1 6

1 31

1 32

1 33

1 34

1 35

1 36

1 37

1 38

6 1

6 30

6 39

6 40

6 41

6 31

6 42

6 32

6 33

6 34

6 35

6 36