Web as Graph – Empirical Studies

1. Web as Graph – Empirical Studies The Structure and Dynamics of Networks

2. Chapter-3 • Broder et al, Graph Structure in the Web. Computer Networks 33,309-320(2000). • Faloutsos et al, On Power-Law Relationships of the Internet Topology. SIGCOMM 1999 • M. E. J. Newman, The Structure of Scientific Collaboration Networks. PNAS 2:98,404-409 (2001)

3. How does it help? • Answer questions like: • What does the internet look like? • Are there any topological properties that don’t change in time? • How will it look like a year from now? • How can I generate Internet-like graphs for my simulations? • Designing crawl strategies on Web. • Understanding sociology of content creation on Web. • Analyzing behavior of Web algorithms using link information. • Predicting evolution of Web structures like bipartite cores, etc. • Predicting emergence of new phenomena in Web graph.

4. Power Law Where, K > 1 Log-log plot of Power Law Power Law plot Scale-free network: “Scale-free networks' structure and dynamics are independent of the system's size N, the number of nodes the system has.” -Wikipedia

5. Examples • Access statistics of web pages, • number of times users at a single site access particular pages, • PageRank of web pages, • In-degree, out-degree of webpages, • Amazon’s online store • Library book records • All preferential attachment models

7. Power Laws Rank Exponent:

8. Power Laws Outdegree Exponent:

9. Power Laws

10. Web Graph

11. Scientific Collaboration Network Similar to Erdös number

12. Scientific Collaboration Network

13. Observations • Newman’s data does not follow Power law • Presumably because the study was conducted for a finite time window of 5 years. • In most of the databases, the largest group occupies around 80-90% of all authors • Authors are very highly connected and • No immediate danger of fragmentation  • 6 degrees of separation holds.