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--- title: "Web Graph" type: concept source: https://www.jemoka.com/posts/kbhweb_graph/ confidence: high status: active --- let’s consider the web as a directed graph, where… a hyper-link denotes perceived relevance (“quality”) anchor of the hyper-link describe the target page (“textual context”) anchor text consider: IBM’s mostly graphical homepage IBM’s copyright page Rival’s span IBM page Consider, a million picees of anchor text saying “IBM” pointing to ibm.com, suddenly, that legitimizes the home page <a href="target">[archor text that says IBM]</a> So, when we index a website, we index not just the website but 1) all links pointing to it and 2) the text of those links. side effects “Google Bombing”—a lot of people artificially increasing the rank of the website by pointing a lot to it on more fake websites and writing in anchor text about the spoofed website solution: weight each web page’s target anchors based on their “authoritativeness”—either curated or calculated. uses of anchor text synonym usage (collect multiple ways of referring to the same website) finding translations (collect multiple languages referring to the same website) providing constituency boundaries (i.e. the anchor text is a NP within the larger sentence) PageRank “A page that’s a very popular is a good page.” Page Rank Solves the LinkCount problem by using the intuition that we want to weight Directed Popularity based on the importance of the page where the link is from. Precisely: after starting at a random page, we walk along each link with equal probability and continue until we reach a time where a page’s visitation rate converges. We will use this as PageRank Teleporting To resolve the problem of dead ends, if we reach a dead end we jump to a random page. Even if we didn’t reach a dead end, with probability \(\alpha\) we still jump to a random page. if the node has no out-link, the transition probability to each other node is \(\frac{1}{N}\) if the node does have \(K\) out links, the probability of telephoning to a random node is \(\frac{\alpha}{N}\), and the probability of going to a normal out link is \(\frac{1-\alpha}{k}\). Building PageRank Matrix For some matrix A, \(A_{ij}\) is \(1\) if there is a hyper-link from \(i\) to \(j\). If row \(A\) has no 1s, then we will replace each element by \(\frac{1}{N}\). For all other rows, divide each row by the sum of the row, and multplying each entry by \((1-\alpha)\). Then, add \(\frac{a}{N}\) to the whole row. calculating PageRank uses the fact that the matrix you built in the previous step is Ergotic to compute its steady state. Link Count page that is pointed to by lots of other pages Failure: this is very easy to spam–we can just create a bunch of pages and add arbitrary number of links. Undirected Popularity “Degree”: number of in links plus the number of out-links. Directed Popularity Number of in-links