## CheiRank versus PageRank

In class we discussed the concept of PageRank, an algorithm used by Google to rank websites: it counts the number and quality of links to determine the importance of the page. Google also uses a different algorithm, CheiRank, which determines the importance of a page based upon its number of outgoing links. The PageRank vector is computed as the eigenvector with the maximum real eigenvalue of a Google Matrix G, a stochastic matrix representing pages and the links between them. The CheiRank is the eigenvector with the maximum real value of a matrix G* built the same way as a Google Matrix except the adjacency matrix uses inverted directions of links. The PageRank algorithm gives a high rank to popular nodes while CheiRank identifies communicative nodes. CheiRank and PageRank both rank each node so the two algorithms give you a two-dimensional ranking of nodes in the network.

The correlation between PageRank and CheiRank differs drastically across different networks. There is a correlation between PageRank and CheiRank in the Wikipedia network, while in most networks the correlation between the two is about zero. The network architecture is not completely revealed from either PageRank or CheiRank algorithms.

In class, we discussed extensively the PageRank algorithm. The CheiRank algorithm gives a different outlook on information flow and what determines a page’s importance.

https://arxiv.org/pdf/1409.0428.pdf