Motivation Similar to Centrality Measures, Link Analysis Methods - IT/Computer Science Assignment Help

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Motivation Similar to centrality measures, link analysis methods allow us to identify the popularity of a vertex, based on the structure of the whole graph. Google uses the link analysis method PageRank to compute the popularity score for each Web page. This score is provided as an indicator as to how high the Web page should be ranked in search results. 300958 Social Web Analytics Outline

1 Random walk on a Graph 2 Random Walk on a Directed Graph 3 PageRank 300958 Social Web Analytics Random Walk A random walk is a traversal of some space, where we take n steps (some number of steps), and each step is decided randomly. Examples of random walks in 1, 2, and 3 dimensional space can be seen at: http://en.wikipedia.org/wiki/Random_walk 300958 Social Web Analytics Random Walk on a Graph Random walks can be taken on graphs, where each step moves us to a vertex and the edges of each vertex provide a path between vertices. Two random walks from v1 of lengthTwo random walks of length 3 starting from v1 shown in red and blue. 300958 Social Web Analytics Random Walk on a Graph and Probabilities By taking a random walk of length 1, we choose an edge at random that is connected to the current vertex and follow it. The probability of following a particular edge is equal to 1/degree(v), starting at vertex v. Probability of arriving at vertex.

After a random walk of length 1 beginning at v1 , the probability of arriving at v2 is 1/4. 300958 Social Web Analytics Random walk probability Problem After a random walk of length 1: What is the probability of arriving at v3, when beginning at v1? What is the probability of arriving at v2, when beginning at v4? What is the probability of arriving at v5, when beginning at v3? ? ? ? ? ? v1 v2 v3 v4 v5 Figure: Random walk of length 1 problem. 300958 Social Web Analytics State distribution The state of a random walk is the vertex in which the walk has ended on. After a random walk of length n, there is a chance of being in multiple states (arriving at multiple vertices), where each state has a probability. The collection of probabilities forms a distribution over the set of states.

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