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Discussion Topic:. Models for Social Networks. Web Science Tea Feb 29, 08. Milena Mihail [email protected] NSF : CDI. Elsewhere :. Yahoo: Raghavan WWW06 Brachman GT talk. Microsoft :

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Milena mihail mihailcc gatech

Discussion Topic:

Models for Social Networks

Web Science Tea

Feb 29, 08

Milena Mihail

[email protected]


Milena mihail mihailcc gatech

NSF : CDI

Elsewhere :

Yahoo: Raghavan

WWW06

Brachman

GT talk

Microsoft:

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

PREAMBLE

What is Web Science ?

Our grassroots discussions :

Includes some intersection of

comp sci, economics, social sci.


Milena mihail mihailcc gatech

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

descriptive/predictive/explanatory/prescriptive

analytic value.


Milena mihail mihailcc gatech

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.


Milena mihail mihailcc gatech

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.


Milena mihail mihailcc gatech

Models for Social Networks

(in this spirit)

PREAMBLE

What is Web Science ?

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?

Our grassroots discussions :

Includes some intersection of

comp sci, economics, social sci.


Milena mihail mihailcc gatech

(nice pictures with some meaning)

Range of Models

Internet (general)

Routing Internet

AS Level

Routing

Level

Sparse Power Law Graphs

with very different assortativity

few long links

in a flat world


Milena mihail mihailcc gatech

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


Milena mihail mihailcc gatech

( Range of Flickr Pictures - meaning ? )

Technology Platforms

Local Facebook Friendship Graph

A Wep Page

Organization

4 Color Theorem


Milena mihail mihailcc gatech

Range of Models

Biological Networks

with unclear meaning,

but make front page

of Nature/Science/PNAS


Milena mihail mihailcc gatech

Range of Models

(nice pictures with no meaning)


Milena mihail mihailcc gatech

Range of Mathematical Models

Rick Durrett, Cornell, Probabilist

n

Matthew Jackson, Staford, Economist


Milena mihail mihailcc gatech

Canonical Example: Modeling the Small World Phenomenon

Clustering

and

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!


Milena mihail mihailcc gatech

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

Theorem:

The only value for which

the network is navigable

isr =2.

14


Milena mihail mihailcc gatech

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

Important to have FLEXIBLE network models

eg in Prediction / Simulation

economics

engineering

Average degree and Degree distribution

Clustering coefficient (small dense subgraphs)

Diameter

Expansion/Conductance

(bottlenecks)

Eigenvalues, eigenvectors

(quantify bottlenecks and find groups efficiently)

Evolving toward monopolies/oligopolies?

Assortativity

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?


Milena mihail mihailcc gatech

Given

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


Milena mihail mihailcc gatech

Example 2: Growth & Preferential Attachment

One vertex at a time

New vertex attaches to

existing vertices


Milena mihail mihailcc gatech

Some evolutionary

random graph models

may also capture more factors,

e.g, geography,

and hence varying conductance.

Example 2, generalization towards flexibility:


Milena mihail mihailcc gatech

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.


Milena mihail mihailcc gatech

Explanatory / Microscopic Models / Incentive Driven

Example: A Network Formation Game

How fast can such a stable configuration be reached?


Milena mihail mihailcc gatech

Hybrid Models

RANDOM DOT PRODUCT GRAPH MODEL


Milena mihail mihailcc gatech

Example 1:


Milena mihail mihailcc gatech

Example 2:


Milena mihail mihailcc gatech

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.


Milena mihail mihailcc gatech

HOW ABOUT YOU ?

WHICH QUESTIONS

DO YOU WANT TO ANSWER ?


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