Small World Networks

More documents

Recommendations

Info

d-Lattice <strong>Networks</strong> ¡ d-Lattice networks are regular d- dimensional k-regular grids of vertices l 1-d, k=2 it’s a ring l 2-d, k=4, it’s a mesh n=36, d=2, k=4 n=16, d=1, k=2 23 Other Examples of d-Lattices n=36, d=2, k=8 n=16, d=1, k=4 24 12
Properties of d-Lattices ¡ For d=1 l L ∝ n à L=(n(n+k-2)) / (2k(n-1)) l |Г i (v)|=k for any v l γ = (3k-6)/(4k-4) e.g., = 0,5 for k=4 ¡ For d=2 l L ∝ √n l |Г i (v)|=k l γ = (4k-16)/(16k-16) e.g. = 0 for k=4 25 Some Actual Data ¡ d=1, n=1000, k=4 l L =125 l γ = 0,5 for k=4 l Good clustering, but not a small world!!! ¡ d=2, n=10000, k=4 l L = 50 l γ = 0 l Not a small world and not clustered ¡ Lattice networks are not small world!!! l Not realistic representations of modern networks 26 13
Page 1 and 2: Small World Networks Franco Zambone
Page 3 and 4: “Hey, it’s a Small World!” ¡
Page 5 and 6: The “Bacon Distance” ¡ ¡ Thin
Page 7 and 8: Part 2 ¡ Modeling Small World Netw
Page 9 and 10: Basic of Graph Modeling (2) ¡ ¡
Page 11: Clustering ¡ ¡ ¡ The clustering
Page 15 and 16: Length of Random Networks ¡ ¡ ¡
Page 17 and 18: Random Networks vs. Real Networks (
Page 19 and 20: Let’s Re-wire! Re-wiring Re-wirin
Page 21 and 22: Experimental Results (3) ¡ Here’
Page 23 and 24: Part 3 ¡ Properties and Dynamics o
Page 25 and 26: Non Linearity of Percolation ¡ In
Page 27 and 28: The Spread of Internet Viruses ¡
Page 29: And more implications… ¡ This ex

Small World Networks

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?