Upgrade Report - Department of Informatics - King's College London

List of Figures1 Erdós-Rényi Graph G(n, p) graph with n = 50000, p = 0.0001 . . . . . . . . . . . . . . . . . . 82 Degree distribution of the preferential attachment graph . . . . . . . . . . . . . . . . . . . . . 103 Degree distribution of the edge copying graph with γ = 0.5 . . . . . . . . . . . . . . . . . . . 104 Degree distribution of the triangle closing graph with random-random selection policy . . . . 115 Degree distribution of the forest fire model with n = 10 5 m = 1, p = 0.6, r = 0.3 . . . . . . . . 126 Random Walk Models (log-log scales). m = 3, s = 200, N = 50000, Power-law Co-Efficient cas noted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Comparison of different parameter effects on undirected random walk graphs N = 50000 . . . 208 Preferential Message Propagation (log-log scales). m = 2,p = 0.2,N = 50000 . . . . . . . . . . 219 Grow-Back Connect-Densify Model(log-log scales). a = b = c = 1 3,p = 0.1,N = 200000 . . . . 2210 Implicit Graph Model. α = 1.25,N = 10000,c = 1.8 . . . . . . . . . . . . . . . . . . . . . . . . 2411 Partitioned Preferential Attachment. n = 7, 5.10 5 , m = 3, s = 500 . . . . . . . . . . . . . . . . 2512 Twitter 2009 data on log-log scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513 (In-degrees, Out-Degrees) to frequency plot on a log scale . . . . . . . . . . . . . . . . . . . . 2614 Degree Distribution of various real networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2715 Degree-Based Cut Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2816 Degree Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2917 Real Twitter data vs crawled data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3018 In Degrees (red) Out Degrees (green) Total Degrees (blue) and tweets (fuchsia) as a functionof frequency on a log scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3119 Real 2009 Twitter distribution (Green) compared to sampled Twitter distribution (Red) . . . 3220 KV test on a preferential attachment graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3321 Plots of experimental data showing cover time of all vertices of degree at least t a as a functionof a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3722 Plots of experimental data showing cover time of all vertices of degree at least t a (ignoringa < 0.25) as a function of a in the SlashDot graph. . . . . . . . . . . . . . . . . . . . . . . . 3823 Plots of experimental data showing cover time of all vertices of degree at least t a (ignoringa < 0.35) as a function of a in a sample of the Google web-graph . . . . . . . . . . . . . . . . 3924 Growth pattern of all methods at 1000,2000,.., 64000 vertices . . . . . . . . . . . . . . . . . . 5225 The comparison of the degree frequency distributions of the different methods at 64000 visitedvertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53IV