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On Distinguishing between Internet Power Law

On Distinguishing between Internet Power Law. B Bu and Towsley Infocom 2002 Presented by. Problem: comparing and generating real graphs. How can we Compare Generate Several metrics exist Several generation approaches exist. Contribution. They propose a new metric

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On Distinguishing between Internet Power Law

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  1. On Distinguishing between Internet Power Law B Bu and Towsley Infocom 2002 Presented by

  2. Problem: comparing and generating real graphs • How can we • Compare • Generate • Several metrics exist • Several generation approaches exist

  3. Contribution • They propose a new metric • Clustering coefficient, that captures “local density” • Using this metric, the evaluate generation methods • Methods are good in matching powerlaws • The do not match clustering property of Internet • They propose a new method to generate graphs • Variationon preferential attachment (Barabasi Albert) • Internet exhibits small world properties

  4. Motivation • Is any motivation provided?

  5. Roadmap • Background • New Metrics • Evaluating graph generators • A new generator • Conclusions

  6. Basic concepts • We study the Internet at the AS level • Data from routeviews and NLANR • Model the network as undirected graph • Topology follows powerlaws • The degree distribution

  7. Clustering coefficient • Attempts to capture the local density: • Is my neighborhood well connected? • Clustering coeef. of a graph G is the average clustering coeff. of its nodes • Note: nodes with one degree are excluded by definition

  8. Characteristic Path length • Attempts to captures the average distance…

  9. Current graph generators • Brite: Barabasi Albert: preferential attachment • AB model: Brite + rewiring of existing links • Inet: enforced powerlaw degree distribution and preferential attachment • PLRG: enforce plaw degree distribution and random matching of nodes

  10. Evaluating graph generators • Generators seem to fail in clustering coefficient

  11. A new generator: GLP • Adding a constant beta in the equation • With probability p: add m new links • With probability 1-p: add a new node with me links

  12. Analysis: provable plaw distribution • Assume degrees a a continuous function thus the probability of joining is the rate of degree increase

  13. Calculating parameters • Given desired node, edges and desired plaw exponenet alpha, find p and beta.

  14. GLP works better

  15. Conclusion • Current generators do not capture all topological aspects: • Specifically localized properties such as clustering • The propose a new generator GLP • Provable powerlaw distribution • Experimentally better clustering

  16. What did I think of the paper • Pros • Cons • Things left to be done…

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