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The algorithms known as PageRank and HITS are the two most prominent examples of network-based ranking methods. These methods require only a little bit of mathematics to understand well. The main underlying model is that the rank of any page is dependent on the number and location of backlinks (or in-links) to that page, and the importance or quality of the pages that contain those backlinks. Most explanations of how this is precisely computed uses the language of linear algebra and “eigenvalues”, which often obscures the relatively simple ideas underlying them.Here is an attempt to make these algorithms more accessible by boiling down the math to the essential details. Let G be a directed graph. We think of the nodes of G as webpages and the directed arcs as hyperlinks. Let A(G)=A be the adjacency matrix where A[i,j] = 1 if (i,j) is an arc, is 0 otherwise. The ith row of A is the (characteristic) vector representing all the out-neighbors of the ith node, and the jth column of A is the vector representing the in-neighbors of the jth node. The transpose matrix A’ has the roles reversed, where the ith row of A’ is the vector representing all the in-neighbors of the ith node, and the jth column of A’ is the vector representing the out-neighbors of the jth node.Matrix multiplication can give simple algebraic representations of graph structures. For example, the square of the adjacency matrix A^2 has as its [i,j]th entry the number of 2-hop paths from ith node to jth node. And the product A’A has as its [i,j]th entry the number of nodes that are common in-neighbors to both the ith and jth node. Note how A’A is a symmetric matrix, likewise AA’ is also symmetric. Symmetric matrices have the property that the [i,j]th entry matches the [j,i]th entry for all pairs i,j.