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the damping factor, Ivan and Gorlmusz (2011) were able to personalize the al- gorithm for 13 different proteins found in the study. Then Ivan and Gorlmusz (2011) applied the personalized algorithm to the human PPI graph HPRD (Hu- man Protein Reference Database). Ivan and Gorlmusz (2011) found that of the proteins with the highest PageRank, 10 out of the 13 proteins that the algorithm was personalized to appeared in the top 22, and another 10 had clear connec- tions to cancer. In a 2013 paper, Bánky, Iván, and Grolmusz introduced a new method that would compensate for the weight that smaller degree nodes compared to larger degree nodes, which are sometimes simply removed from the analysis to pre- vent them from overwhelming the smaller nodes. Bánky et al. (2013) showed that in undirected graphs, the PageRank of a node is proportional to its degree if the personalization vector was proportional. The PageRank with a personal- ization vector w such that: (d(v1) d(v2) d(vn))T w = 2|E| , 2|E| , ..., 2|E| , (VI.3) Where d(vi) is the degree of vertex vi and |E| is the number of edges in the graph, is equal to w for undirected graphs. This allowed Bánky et al. (2013) to factor out the relative degreeness from each vertex. In order to use a similar method for directed graphs, Bánky et al. (2013) defined the personalization vector w: (dr(v1) dr(v2) dr(vn))T w= |E| , |E| ,..., |E| , (VI.4) 32PDF Image | MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM
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