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LIST OF FIGURES Figure 1.1 Figure 1.2 Figure 1.3 Figure 1.4 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 3.1 Figure 3.2 Figure 3.3 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 A pictorial illustration of the PageRank model 2 Relationships between web pages and graphs 5 PageRank with a random variable as the teleportation parameter 8 Performance of the PageRank algorithm 9 PageRank papers by year 11 Overview of PageRank formulations Gauss-Seidel vs. the power method Strong component PageRank mass A PageRank function 36 13 25 29 Valid Taylor steps 48 PageRank derivative magnitude Relative magnitude of the PageRank derivative 52 Empirically measured teleportation coefficients 71 The framework for Gauss quadrature error analysis The Gauss quadrature error analysis applied to PageRank 81 PageRank magnitude for a complex damping parameter 82 Quadrature convergence with extreme endpoint 82 Convergence of algorithms for RAPr 84 Timing for the RAPr algorithms 85 Intersection similarity between PageRank and the RAPr model 89 Standard deviation and spam 91 Performance of the inner-outer iteration with varied β and η 105 Performance of the PageRank algorithm 106 65 Path damping coefficients for the Random Alpha PageRank model 69 Parallel performance of the inner-outer iteration Inner-Outer preconditioner spectrum 111 Inner-Outer error analysis for a small graph Compressed row and column storage 120 MatlabBGL architecture 123 Binary trees as arrays 131 Performance of the gaimc library 136 xvii 109 115 52 Differences between PageRank and the Random Alpha PageRank model 56 An example of the Random Alpha PageRank model 58 Inverse Gaussian density 60 Beta distributions and Random Alpha PageRank vectors 80PDF Image | ALGORITHMS FOR PAGERANK SENSITIVITY DISSERTATION
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