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tein interaction networks contained many false negative and positive interaction edges. Ivan and Gorlmusz (2011) gave the stability estimation of PageRank as: ||p−pˆ||1 ≤ c pj (VI.2) 2(1 − c) ∑ Where the ith coordinate of vector p gives the PageRank of vertex i, and vector pˆ gives the PageRank of the vertices after the edges with endpoints in set U are changed. Therefore, if only the edges between the less important nodes are changed, then the effects of the change on the PageRank remain low. This was important because of the often unreliable mapping of less important protein interactions. Because the PageRank algorithm works with a directed graph, Ivan and Gorl- musz (2011) used it with a metabolic graph, where nodes represent chemical reactions and are connected with a directed edge if one reaction produces a product that is used by another reaction. After computing the PageRank for the metabolic graph of Mycobacterium tuberculosis, Ivan and Gorlmusz (2011) were able to identify nodes that were of special interest. These nodes were chemical reactions that had a PageRank that was larger than proportional to their degree, which meant that in a random walk they are hit more often than others with the same network degree. This means that, similar to how Chen et al. (2007) used it to find lesser known but still very important scientific papers, Ivan and Gorl- musz (2011) were able to identify important chemical reactions that did not have a large number of links to other reactions. Ivan and Gorlmusz (2011) also wanted to investigate protein-protein inter- action (PPI) networks, which are undirected graph networks where the nodes are proteins and the edges are interactions between them. Ivan and Gorlmusz (2011) were able to use the personalized PageRank also developed by Brin et al. (1999) to analyze the proteomics data of melanoma patients. By adjusting 31 j∈UPDF Image | MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM
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