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many couples of nodes, and removal according to dominators, where one node is dominated by another if every path from the root to itself contains the other, so that if the other goes extinct then it must as well. Allesina and Pascual (2009) applied these algorithms to 12 published food webs. To compare these results, they programmed a genetic algorithm to find the best possible sequence with an evolutionary search, which has been shown to be effective although computationally expensive. Compared to the genetic algorithm, most of the methods did not perform well. The majority did not match the effectiveness of the genetic algorithm. Of the ones that were comparable, the removal procedure based on dominators only did as well 2/3 of the time, but the PageRank algorithm matched the genetic algorithm 11 out of 12 times. In an attempt to further improve the PageRank method, Allesina and Pas- cual (2009) reclassified some of the links in the food web as either ”redundant” or ”functional” based upon their effects on secondary extinctions. By remov- ing the redundant connections, Allesina and Pascual (2009) built a simplified food web that was just as robust as the original. When the PageRank algo- rithm was tested with this, the results matched the genetic algorithm. With this, Allesina and Pascual (2009) were able to provide an effective algorithm to rank species importance in the food web, and show that it was much more effective that counting the number of connections. 6.3 Protein Networks Ivan and Gorlmusz (2011) applied the PageRank algorithm to protein inter- action networks. Ivan and Gorlmusz (2011) demonstrated it on the metabolic network data of the tuberculosis bacterium and the proteomics analysis of the blood of melanoma patients. Ivan and Gorlmusz (2011) used the PageRank algorithm, stating one of its best attributes being its stability, because the pro- 30PDF Image | MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM
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