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Youth group example.

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    People, Here is an example of PageRank applied to a youth group. Enclosed is an Excel matix file showing voters rows intersecting votees columns. From:
    Message 1 of 1 , Sep 1, 2005
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      People,

      Here is an example of PageRank applied to a youth group. Enclosed is an Excel matix file showing voters' rows intersecting votees' columns. From: http://groups.yahoo.com/group/sd-2/message/319

      -----------------------------

      People,
      Curiosity got the best of me and I analyzed Timur's modified dataset[...]

      Number of votes and PageRank scores:

      3-Nawab, 5, 16.6%
      5-Rehmat, 2, 12.5%
      4-Iqbal, 3, 11.7%

      2-Shauket, 9, 11.3%
      6-Akram, 3, 10.6%
      7-Zaffar, 5, 8.1%

      8-Shahbaz, 3, 6.9%
      9-Haider, 2, 5.2%
      15-Mehmood, 3, 3.7%

      16-Sardar, 2, 2.5%
      10-Sohail, 2, 2.2%
      13-Khalid, 1, 1.99%

      11-Farooq, 3, 1.97%
      14-Tareq, 2, 1.97%
      17-Gul, 1, 1.5%
      12-Sharafat, 1, 1.3%

      This data is less centralized than Denis's data below, and it is very well connected with total participation and two or more votes per person. Nawab is the clear winner here, and the most popular person, Shauket, is at fourth place with no direct power(though he has enough indirect power[in an SD2 environment] to shift relative ranks by changing his votes.)

      Compared with Denis's network, it also has more differential between
      indegree(vote count) and PageRank scores. Our second ranked man,
      Rehmat, has recieved only two votes, yet he has beat Shauket with 9
      votes because Rehmat recieved his votes from the highly ranked Nawab
      and Akram.[...]
      --------------------------------------

      For simplicity's sake, I will focus on Rehmat.

      Nawab's rank = 16.6%, Akram's rank = 10.6% 

      Nawab voted for three people, one of which was Rehmat, so applying the formula "out-vote strength = rank / # of out-votes", this is:

      16.6%/3 = 5.5%; this is the strength of the vote going from Nawab to Rehmat.

      Likewise, Akram voted for three people, so the strength of one of his outvotes is: 10.6%/3 = 3.53%

      Average in-vote strength would be calculated: (5.5%+3.53%)/2 =

      9.03%/2 = 4.01%

      Using the formula of "rank = (avg. in-vote strength) X # of votes", Rehmat's rank should be:

      4.01% X 2 = 8.02%

      This differs from the posted 12.5%, which may indicate a data-entry problem. The point here is to go through the motions to validate the results with the formula, to show PageRank outputs, and to show that there is enough transparency to lead to troubleshooting.

      For those who want to play with PageRank calculations, here is a link: 

      http://webworkshop.net/pagerank_calculator.php

      shanti

      Mark, Seattle

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