Discussion on Random Walks

# Discussion on Random Walks - Disc ussion on Ra ndom W a lks...

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2/10/14 Discussion on Random Walks www.cs.bu.edu/~best/courses/cs109/modules/randomwalks/ 1/5 Graph Random Walks Goals: Review the basics of graph random walks Work through an example showing how it can be solved via simulation Show the link between random walks and the PageRank algorithm Work through a series of examples using the PageRank simulator Consider the pitfalls of PageRank Plan: a. Recall that in a random walk, an individual walker follows the process below: 1. Start in some random node 2. At random select one of the outgoing edges of the current node 3. Walk over that edge to a new node 4. Go to 2 Note that in general the edges out of a node may be labeled with the probability that they would be selected by the walker (i.e., the edges do not have to be equally likely selected). b. In general, we are interested in how a very large number of walkers (a population of walkers) would end up covering the various nodes in the graph. The particular question we want to answer is to figure out the proportion (percentage) of the population at each node after having the walkers roam the graph for a very long time. Thus, for a node X, we want to find Pr(X). c. Recall that one way to do this (as we have done in class) is to establish relationships between the proportion of the population at each node, noting that they must all add up to 100%. Use the example below (which I showed in lecture but did not solve) to derive these relationships.

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2/10/14 Discussion on Random Walks www.cs.bu.edu/~best/courses/cs109/modules/randomwalks/ 2/5 d.
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