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Discussion Topic:. Models for Social Networks. Web Science Tea Feb 29, 08. Milena Mihail mihail@cc.gatech.edu. NSF : CDI. Elsewhere :. Yahoo: Raghavan WWW06 Brachman GT talk. Microsoft :

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Discussion Topic:

Models for Social Networks

Web Science Tea

Feb 29, 08

Milena Mihail



Elsewhere :

Yahoo: Raghavan



GT talk


New Cambridge Lab

Jennifer Chayes

Our non grassroots discussions :

Super-Duper Data Center,

ala Jeanette Wing

Should revisit this point,

in view of NSF-Google-IBM ?

Chris Klaus

GT talk


What is Web Science ?

Our grassroots discussions :

Includes some intersection of

comp sci, economics, social sci.

Parenthesis: MSN SemGrail 07

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


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

Dynamics, emergent systems, social networks

Requires new analytics (eg what are right logics,

probabilistic and approximation metrics)

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.

Models for Social Networks

(in this spirit)


What is Web Science ?


Wide Range of Models

Canonical Example: Modeling Small World Phenomenon

Model Parameters/Metrics and their Relevance

Models : Structural

Explanatory (Optimization or Incentive Driven)


Which question are you (am I) trying to answer?

Our grassroots discussions :

Includes some intersection of

comp sci, economics, social sci.

(nice pictures with some meaning)

Range of Models

Internet (general)

Routing Internet

AS Level



Sparse Power Law Graphs

with very different assortativity

few long links

in a flat world

Range of Models

(nice pictures with some meaning)

Patent / co-author network

in Boston area

notice bottleneck bad cut

Flickr social network

from Flickr

search keyword “graph”

notice no botlleneck bad cut

( Range of Flickr Pictures - meaning ? )

Technology Platforms

Local Facebook Friendship Graph

A Wep Page


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

Canonical Example: Modeling the Small World Phenomenon



Small Diameter

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.

Kleinberg 90’s: Navigability !

These short paths can be found efficiently with local search!

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 ?

Kleinberg’s navigability model


The only value for which

the network is navigable

isr =2.


Model Parameters/Metrics (as a function of n) and their Relevance

Important to have FLEXIBLE network models

eg in Prediction / Simulation



Average degree and Degree distribution

Clustering coefficient (small dense subgraphs)




Eigenvalues, eigenvectors

(quantify bottlenecks and find groups efficiently)

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?


Choose random perfect matching over

Structural / Macroscopic Models

Random graphs with desirable graph properties,

thought to be aggregating all microscopic primitives

Example 1: Power Law Random Graph

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?

Hybrid Models


Example 1:

Example 2:


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.




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