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Comparing and Generating Realistic Graphs: Introducing the GLP Method

This paper presented at Infocom 2002 focuses on distinguishing between various internet power law models, providing a new metric - clustering coefficient, evaluating generation methods' ability to match power laws vs. clustering properties. The proposed GLP method enhances clustering and offers a provable power law distribution. The study uses AS-level Internet data, models networks as undirected graphs following power laws, and measures the clustering coefficient and characteristic path length. Current generators are found lacking in capturing clustering, leading to the introduction of GLP for better performance in generating realistic networks.

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Comparing and Generating Realistic Graphs: Introducing the GLP Method

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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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