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…