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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Discussion on Random Walks
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 Spring '13
 AzerBestavros
 se s/c s109/module, s/c s109/module s/r, s.bu.e du/~be st/c

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