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Other applications of PageRank

From class we saw that PageRank was used to rank nodes in a graph based on network measures. Designed by Google founders, PageRank is an algorithm designed to use the structure of the internet to determine the relative relevance of each page in the internet. It assigns a numerical rank to each indexed web page, evaluating the link structure of each web page. If some page A has a link to page B, this can be interpreted as page A giving its importance, credibility, or votes towards page B. Though this algorithm was popularized as an internet search algorithm, the power behind the idea of ranking things increased the variety in the contexts to which PageRank has been applied to.

The intuition behind the PageRank algorithm are generic, so PageRank can be applied to the social network graph of Twitter’s follower relations. One way to use PageRank is to represent each user and each tweet by a node. Then draw links between two users A,B if A follows B or if user A retweets some tweet t. This method gives a rank for each tweet in the network, and by extension could give some rank for important users as they would be the ones with important tweets.

In the same vein of ranking a set of items, consider recommendation systems. Fundamentally, recommendation systems want to suggest new content for each user based on their interests and interests of other similar users. After building out a network connecting users to movies they have watched, we can then user random walks starting at desired users. At every step, the walker either moves to one of the neighbors of the current node or jumps back to the start node. If this is done enough times this will eventually give an approximation of the steady-state probability of the walker being in each of the nodes ie the eigenvector.


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