1 Milena Mihail Web Science Tea Feb 29, 08 Discussion Topic:

What is Web Science ? Includes some intersection of comp sci, economics, social sci. Our grassroots discussions : Microsoft: New Cambridge Lab Jennifer Chayes Yahoo: Raghavan WWW06 Brachman GT talk Chris Klaus GT talk NSF : CDI Elsewhere : Our non grassroots discussions : Super-Duper Data Center, ala Jeanette Wing Should revisit this point, in view of NSF-Google-IBM ?

What is Web Science ? The study of the WWW, broadly defined. By virtue of the pervasiveness of the object of study. Systems-like science (like chemistry or biology). As opposed to “computer science” which is the study of “computation”, biology is the study of “life” from the cell to evolution to animals…. Should be studied in terms of its descriptive/predictive/explanatory/prescriptive analytic value. Parenthesis: MSN SemGrail 07

Why should there be Web Science ? Encourage collaboration across different areas. Something between the union and intersection of several areas. Need to establish common vocabulary, goals, problems. “Understanding the elephant versus the tail trunk”. Educate students for industry. Encourage academia to understand the study of the Web as a discipline. Parenthesis: MSN SemGrail 07

Themes cutting across subareas of Web science Long Tails / Economics / Culture Fractal Nature, multi-scale Humans and machines interact and interactions registered. New dimension in social sciences. Transformed way we think about information (analogy to introduction of printing press). Democracy of information, producers and consumers of information coincide. Dynamics, emergent systems, social networks Requires new analytics (eg what are right logics, probabilistic and approximation metrics) Parenthesis: MSN SemGrail 07

What is Web Science ? Includes some intersection of comp sci, economics, social sci. Our grassroots discussions : (in this spirit) Outline: Wide Range of Models Canonical Example: Modeling Small World Phenomenon Model Parameters/Metrics and their Relevance Models : Structural Explanatory (Optimization or Incentive Driven) Hybrid Which question are you (am I) trying to answer?

Range of Models Internet (general)Routing Internet AS Level Routing Level (nice pictures with some meaning) few long links in a flat world Sparse Power Law Graphs with very different assortativity

Range of Models Patent / co-author network in Boston area (nice pictures with some meaning) Flickr social network from Flickr search keyword “graph” notice bottleneck bad cut notice no botlleneck bad cut

( Range of Flickr Pictures - meaning ? ) Technology Platforms Local Facebook Friendship Graph A Wep Page Organization 4 Color Theorem

Range of Models Biological Networks with unclear meaning, but make front page of Nature/Science/PNAS

Range of Models (nice pictures with no meaning)

Range of Mathematical Models Rick Durrett, Cornell, Probabilist Matthew Jackson, Staford, Economist n

Canonical Example: Modeling the Small World Phenomenon Milgram’s Experiment 60’s : Even though relationships are highly clustered, most people are pairwise reachable via short paths, “Six Degrees of Separation” (for fun, see also Facebook group) Strogatz&Watt’s Model 80’s: In a clustered graph of size n, a few random links decrease the diameter to logn. Clustering and Small Diameter Kleinberg 90’s: Navigability ! These short paths can be found efficiently with local search!

14 Kleinberg’s navigability model Theorem: The only value for which the network is navigable is r =2. Are there natural network models which are navigable and have, eg, power-law degree distributions ? Are there natural models where the threshold is not sharp ?

Model Parameters/Metrics (as a function of n) and their Relevance Average degree and Degree distribution Clustering coefficient (small dense subgraphs) Diameter Expansion/Conductance (bottlenecks) Eigenvalues, eigenvectors (quantify bottlenecks and find groups efficiently) eg in Prediction / Simulation economics engineering Evolving toward monopolies/oligopolies? Can it be searched, crawled efficiently? Can pagerank be computer efficiently? Can it route with low congestion? Does it support efficient info retrieval? How does information/technology spread? Important to have FLEXIBLE network models Assortativity

Structural / Macroscopic Models Random graphs with desirable graph properties, thought to be aggregating all microscopic primitives Example 1: Power Law Random Graph Given Choose random perfect matching over

Example 2: Growth & Preferential Attachment One vertex at a time New vertex attaches to existing vertices

Some evolutionary random graph models may also capture more factors, e.g, geography, and hence varying conductance. Example 2, generalization towards flexibility:

Explanatory / Microscopic Models / Optimization Driven Example: HOT, evolutionary, new node attaches by minimizing cost and maximizing quality of service Point: Optimization primitives can yield power law distributions.

Explanatory / Microscopic Models / Incentive Driven Example: A Network Formation Game How fast can such a stable configuration be reached?

RANDOM DOT PRODUCT GRAPH MODEL Hybrid Models

Example 1:

Example 2:

24 SUMMARY It is important to identify critical metrics and parameters ie, how they impact network performance. It is important to develop models where critical parameters vary and flexible network models. It is important to identify network primitives related to optimization and incentives. It is important to develop mechanisms that affect such primitives.

HOW ABOUT YOU ? WHICH QUESTIONS DO YOU WANT TO ANSWER ?