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Yan and Ding (2010) explored more with the algorithm by applying it to co- authorship network analysis in the informetrics community. Yan and Ding (2010) worked to measure both the authors’ academic impact via citation count, as well as their community impact, via co-authorship of papers. By measuring their community impact, Yan and Ding sought to quantify an author’s social capital. Yan and Ding extended PageRank by integrating both the community impact through co-authorship and their academic impact through citations. For a co-authorship network, a node represents an author, edges repre- sent the coauthor relation, and the weight of each edge is the number of co- authorships between each author. Through Yan and Ding’s modification of the PageRank algorithm, they obtained the formula: CC(p) ∑k PR_W(pi) PR_W(p) = (1 − d)∑N CC(pj) + d C(pi) (V.1) j=1 i=1 The main adjustment in this equation is the substitution of N1 , where N is the number of nodes in the network, with ∑ CC(p) , where CC(p) is the number Nj=1 CC(pj) of citations pointing to the author p, and ∑Nj=1 CC(pj) is the citation count of all nodes in the network. This weighs the algorithm toward authors with higher citation counts. By adjusting the damping number d, Yan and Ding adjust the weight given to the citation ranking versus the weight given to the coauthorship value. Since Yan and Ding incorporated citation count into their algorithm, it was not a suitable criterion for evaluating their findings. Instead, Yan and Ding com- pared the results of their algorithm’s rankings of authors to the program commit- tee (PC) membership data for 12 International Society for Scientometrics and Informetrics (ISSI) conferences and by comparing how many had received the Derek de Solla Price Award. Yan and Ding found that the P R_W algorithm was 25PDF Image | MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM
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