random walk. 5 0 50 100 150 0 1 2 3 4 5 6 7 8x 10 −3 Node Degree P ro ba bi lit y of S el ec tio n (a) Simple Random Walk 0 50 100 150 0 0.2 0.4 0.6 0.8 1 1.2 1.4x 10 −3 Node Degree P ro ba bi lit y of S [...] the log- 9 200 500 1000 2.5 3 3.5 4 4.5 5 5.5 6x 10 6 Number of Peers H ig he st o rd er s ta tis tic Centralized Distributed Population Percentile 200 500 1000 2000 10 2 10 3 10 4 10 5 10 6 Number of Peers [...] to a centralized scheme. 85 90 95 2 3 4 5 6 x 10 6 Percentile H ig he st o rd er s ta tis tic Centralized Distributed Population Percentile 0.8 0.85 0.9 0.95 10 2 10 3 10 4 10 5 10 6 Percentile M es sa ge …