CSE 494/598Lecture-9:Social Networks and their applications to WebLYDIA MANIKONDA HTTP://WWW.PUBLIC.ASU.EDU/~LMANIKON /

**Content adapted from last year’s slides

Announcements• Homework-2 soon will be released

• Surprise quiz today!

Today’s lecture• Social Networks – Network theory and concepts – General Introduction

• Hands-on Tutorial -- Crawling Twitter

Networks – Physical & Cyber

Typhoid Mary(Mary Mallon)

Patient Zero(Gaetan Dugas)

Applications of Network Theory• World Wide Web and hyperlink structure

• The Internet and router connectivity

• Collaborations among…– Movie actors

– Scientists and mathematicians

• Sexual interaction

• Cellular networks in biology

• Food webs in ecology

• Phone call patterns

• Word co-occurrence in text

• Neural network connectivity of flatworms

• Conformational states in protein folding

Web Applications of Social Networks• Analyzing Influence or Importance• Page Rank • Related to recursive in-degree computation

• Discovering Communities• Finding near-cliques

• Analyzing Trust • Propagating trust

• Using propagated trust to fight spam• In email

• In web page ranking

• Analyzing Information Diffusion• Modeling web interactions

People are represented as nodes.

Society as a graph

People are represented as nodes.

Relationships are represented as edges.

(Relationships may be acquaintanceship, friendship, co-authorship, etc.)

Society as a Graph

People are represented as nodes.

Relationships are represented as edges.

(Relationships may be acquaintanceship, friendship, co-authorship, etc.)

Allows analysis using tools of mathematical graph theory

Society as a Graph

Graphs – Sociograms (based on Hanneman, 2001)

Graphs – Network analysis uses one kind of graphic display that consists of points (nodes) to represent actors and lines (edges) to represent the ties or relations.

Sociograms – Called by Sociologists; Same as graphs

Strength of ties:

• Nominal – represents presence of absence of a tie

• Signed – represents a negative tie, positive tie or no tie

• Ordinal – represents whether a tie is the strongest, next strongest, etc.

• Valued – measured on an interval or ratio level

ConnectionsSize

◦ Number of nodes

Density ◦ Number of ties that are present/the amount of ties that could be present

Out-degree

◦ Sum of connections from an actor to others

In-degree

◦ Sum of connections to an actor

DistanceWalk

◦ A sequence of actors and relations that begins and ends with actors

Geodesic distance

◦ The number of relations in the shortest possible walk from one actor to another

Maximum flow

◦ The amount of different actors in the neighborhood of a source that lead to pathways to a target

Centrality

◦ This indicates the most important vertices within a graph

Degree◦ Sum of connections from or to an actor

◦ Transitive weighted degreeAuthority, hub, pagerank

Closeness centrality◦ Distance of one actor to all others in the network

Betweenness centrality◦ Number that represents how frequently an actor is between other actors’

geodesic paths

Some Measures of Power & Prestige(based on Hanneman, 2001)

Cliques and Social Roles (based on Hanneman, 2001)

Cliques ◦ Sub-set of actors

◦ More closely tied to each other than to actors who are not part of the sub-set

◦ (A lot of work on “trawling” for communities in the web-graph)

◦ Often, you first find the clique (or a densely connected subgraph) and then try to interpret what the clique is about

Social roles ◦ Defined by regularities in the patterns of relations among actors

Outline•Small Worlds

•Random Graphs

•Alpha and Beta

•Power Laws

•Searchable Networks

•Six Degrees of Separation

Small worlds

Trying to make friends

Kentaro

Trying to make friends

Kentaro

BashMicrosoft

Trying to make friends

Kentaro Ranjeet

BashMicrosoft Asha

Trying to make friends

Kentaro Ranjeet

Bash

Sharad

Microsoft Asha

New York CityYale

Ranjeet and I already had a friend in common!

I didn’t have to worry…

Kentaro

Bash

Karishma

Sharad

Maithreyi

Anandan

Venkie

Soumya

It’s a small world after all!

Kentaro Ranjeet

Bash

Karishma

Sharad

Maithreyi

Anandan Prof. Sastry

Venkie

PM Manmohan Singh

Prof. Balki

Pres. Kalam

Prof. Jhunjhunwala

Dr. Montek SinghAhluwalia

Ravi

Dr. Isher Judge Ahluwalia

Pawan

Aishwarya

Prof. McDermott

Ravi’sFather

AmitabhBachchan

Prof.Kannan

Prof. Prahalad

Soumya

NandanaSen

Prof. AmartyaSen

Prof. Veni

Rao

The Kevin Bacon GameInvented by Albright College students in 1994:

◦ Craig Fass, Brian Turtle, Mike Ginelly

Goal: Connect any actor to Kevin Bacon, by linking actors who have acted in the same movie.

Oracle of Bacon website uses Internet Movie Database (IMDB.com) to find shortest link between any two actors:

http://oracleofbacon.org/

Boxed version of theKevin Bacon Game

The Kevin Bacon Game

Kevin Bacon

An Example

Tim Robbins

Om Puri

Amitabh Bachchan

Yuva (2004)

Mystic River (2003)

Code 46 (2003)

Rani Mukherjee

Black (2005)

Perhaps the other path is deemed more diverse/ colorful…

…actually Bachchan has a Bacon number 3

Total # of actors in database: ~550,000

Average path length to Kevin: 2.79

Actor closest to “center”: Rod Steiger (2.53)

Rank of Kevin, in closeness to center: 876th

Most actors are within three links of each other! Center of Hollywood?

The Kevin Bacon Game

Erdős Number (Bacon game for Brainiacs )

Number of links required to connect scholars to Erdős, via co-authorship of papers

Erdős wrote 1500+ papers with 507 co-authors.

Jerry Grossman’s (Oakland Univ.) website allows mathematicians to compute their Erdosnumbers:

http://www.oakland.edu/enp/

Connecting path lengths, among mathematicians only:

◦ average is 4.65◦ maximum is 13

Paul Erdős (1913-1996)

Unlike Bacon, Erdos has better centrality in his network

Erdős NumberPaul Erdős

Dimitris Achlioptas

Bernard Schoelkopf

Kentaro Toyama

Andrew Blake

Mike Molloy

Toyama, K. and A. Blake (2002). Probabilistic tracking with exemplars in a metric space. International Journal of Computer Vision. 48(1):9-19.

Romdhani, S., P. Torr, B. Schoelkopf, and A. Blake (2001). Computationally efficient face detection. In Proc. Int’l. Conf. Computer Vision, pp. 695-700.

Achlioptas, D., F. McSherry and B. Schoelkopf. Sampling Techniques for Kernel Methods. NIPS 2001, pages 335-342.

Achlioptas, D. and M. Molloy (1999). Almost All Graphs with 2.522 n Edges are not 3-Colourable. Electronic J. Comb. (6), R29.

Alon, N., P. Erdos, D. Gunderson and M. Molloy (2002). On a Ramsey-type Problem. J. Graph Th. 40, 120-129.

Six Degrees of SeparationThe experiment:

Random people from Nebraska were to send a letter (via intermediaries) to a stock broker in Boston.

Could only send to someone with whom they were on a first-name basis.

Among the letters that found the target, the average number of links was six.

Milgram (1967)

Stanley Milgram (1933-1984)

Many “issues” with the experiment…

Some issues with Milgram’s setupA large fraction of his test subjects were stockbrokers

◦ So are likely to know how to reach the “goal” stockbroker

A large fraction of his test subjects were in Boston◦ As was the “goal” stockbroker

A large fraction of letters never reached ◦ Only 20% reached

Six Degrees of Separation

John Guare wrote a play called Six Degrees of Separation, based on this concept.

Milgram (1967)

“Everybody on this planet is separated by only six other people. Six degrees of

separation. Between us and everybody else on this planet. The president of the United

States. A gondolier in Venice… It’s not just the big names. It’s anyone. A native in a rain

forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail

of six people…”

Today• PageRank algorithm

• Introduction to Social Networks

In-class exercise: Crawling WebUSING TWITTER API