Agenda: Tuesday, Jan 25

• Reports from the Field:– Friendster, Love and Money : Monday NY Times (Katy Keenan)– That’s Soooo High School : Monday MSNBC (Jake Wiseman)– BitTorrent: Today’s DP

• Updates on course web page– TA office hours– New readings

• Quick tips on NW Construction task– search and automation tools– ”inherently pairwise” edges– try to avoid complete networks– recall Task 1 write-up due start of Thursday’s class

• ~10 minutes for a little Lifester “social interaction”– you need to remember your Lifester UserID!

• come up front if you forgot– must have registered and created 3 links by 6 PM today

• Contagion, Tipping and Networks: Lecture 1 of 2– based on Gladwell and supplementary material

Contagion, Tipping and Networks

Networked LifeCSE 112

Spring 2005Prof. Michael Kearns

Gladwell, page 7:

“The Tipping Point is the biography of the idea… that the best way to understand the emergence of fashion trends, the ebb and flow of crime waves, or the rise in teen smoking… is to think of them as epidemics. Ideas and products and messages and behaviors spread just like viruses do…”

…on networks.

Some Tipping Examples

• Hush Puppies:– almost dead in 1994; > 10x sales increase by ’96– no advertising or marketing budget– claim: “viral” fashion spread from NY teens to designers– must be certain connectivity and individuals

• NYC Crime:– 1992: > 2K murders; < 770 five years later– standard socio-economic explanations:

• police performance, decline of crack, improved economy, aging…

– but these all changed incrementally – alternative: small forces provoked anti-crime “virus”

• Technology tipping: fax machines, email, cell phones

• “Tipping” origins: 1970’s “white flight”

Key Characteristics of Tipping(according to Gladwell)

• Contagion:– “viral” spread of disease, ideas, knowledge, etc.– spread is determined by network structure– network structure will influence outcomes

• who gets “infected”, infection rate, number infected

• Amplification of the incremental:– small changes can have large, dramatic effects

• network topology, infectiousness, individual behavior

• Sudden, not gradual change:– phase transitions and non-linear phenomena

size of police force

crim

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ate

linear

size of police force

crim

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ate

linear

size of police force

crim

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size of police force

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nonlinear, gradual decay nonlinear, tipping

Rates of Growth and Decay

Gladwell’s Three Sources of Tipping

• The Law of the Few (Messengers):– Connectors, Mavens and Salesman– Hubs and Authorities

• The Stickiness Factor (Message):– The “infectiousness” of the “message” itself– Still largely treated as a crude property of transmission

• The Power of Context:– global influences affecting messenger behavior

Case Study: Baltimore Syphilis Epidemic

• Mid-90’s: sudden increase in syphilis in Baltimore• Three plausible explanations:

– increased crack usage altered sexual behavior• an incremental change in overall context of behavior

– diminished medical services longer time to treatment• an incremental change in the stickiness of the disease

– housing project demolition migration of infected• an incremental change in connectivity (law of the few)

• Any or all could be right

Agenda: Thursday, Jan 27

• Turn Network Construction Project Task 1 write-up now• Examination of initial Lifester network

– in-class experiment on Tuesday

• Completion of “Contagion, Tipping and Networks”

diameter:worst-case: 5average: 2.86

The Small World of Lifester

• So already you have managed to create a network with small diameter

• But can you find the short paths?• Tuesday’s class:

– please print out and bring the profiles of all your Lifester neighbors– please review those profiles before coming to class– we’ll do an in-class experiment on distributed navigation in networks

“Epidemos”[Thanks to Sangkyum Kim]

• Forest fire simulation:– grid of forest and vacant cells– fire always spreads to adjacent four cells

• “perfect” stickiness or infectiousness– connectivity parameter:

• probability of forest– fire will spread to connected component of source– tip when forest ~ 0.6– clean mathematical formalization (e.g. fraction burned)

• Viral spread simulation:– population on a grid network, each with four neighbors– stickiness parameter:

• probability of passing disease– connectivity parameter:

• probability of adding random (long-distance) connections– no long distance connections: tip at stickiness ~ 0.3– at rewiring = 0.5, often tip at stickiness ~ 0.2

Some Remarks on the Demos

• Connectivity patterns were either local or random– will eventually formalize this model– what about other/more realistic structure?

• Tipping was inherently a statistical phenomenon– probabilistic nature of disease spread– probabilistic nature of connectivity patterns– model likely properties of a large set of possible outcomes– can model either inherent randomness or variability

• Formalizing tipping in the forest fire demo:– might let grid size N infinity, look at fixed values of p– is there a threshold value q:

• p < q expected fraction burned < 1/10• p > q expected fraction burned > 9/10

Small Worlds and the Law of the Few

• Gladwell’s “Law of the Few”:– a “small” number of “highly” connected vertices ( heavy tails)– inordinate importance for global connectivity ( small diameter)

• Travers & Milgram 1969: classic early social network study– destination: a Boston stockbroker; lived in Sharon, MA– sources: Nebraska stockbrokers; Nebraska and Boston “randoms”– forward letter to a first-name acquaintance “closer” to target– target information provided:

• name, address, occupation, firm, college, wife’s name and hometown• navigational value?

• Basic findings:– 64 of 296 chains reached the target– average length of completed chains: 5.2

• interaction of chain length and navigational difficulties– main approach routes: home (6.1) and work (4.6)– Boston sources (4.4) faster than Nebraska (5.5)– no advantage for Nebraska stockbrokers

The Connectors to the Target• T & M found that many of the completed chains passed through

a very small number of penultimate individuals– Mr. G, Sharon merchant: 16/64 chains– Mr. D and Mr. P: 10 and 5 chains

• Connectors are individuals with extremely high degree– why should connectors exist?– how common are they?– how do they get that way? (see Gladwell for anecdotes)

• Connectors can be viewed as the “hubs” of social traffic• Note: no reason target must be a connector for small worlds• Two ways of getting small worlds (low diameter):

– truly random connection pattern dense network– a small number of well-placed connectors in a sparse network

• Let’s revisit our Gladwell estimate of class connectivity and MK’s NW

A Mathematical Digression

• We’ve been bouncing around the idea that connectors (~high degree vertices) lead to small diameter

• Obviously, if everyone is connected to everyone else…• But there’s often a limit to the largest possible degree

– you can’t have an unbounded number of friends, colleagues, etc.• May be constraints on the mere existence of certain NWs

– let be the largest degree allowed• why? e.g. because there is a limit to how many friends you can have

– suppose we are interested in NWs with diameter D (or less)• why? because many have claimed that D is often small

– let N(D) = size of the largest possible NW obeying and D• Exact form of N(,D) is notoriously elusive

– but known that it is between (/2)^D and 2^D• So, for example, if we want N ~ 300M (U.S. population):

– if = 150 (e.g. see Gladwell) and D = 6 (6 degrees): NW exists– D = 6, N = 300M, solve 2^D > N: get > 23

Small Worlds: A Modern Experiment

• The Columbia Small Worlds Project:– considerably larger subject pool, uses email– subject of Dodds et al. assigned paper

• Basic methodology:– 18 targets from 13 countries– on-line registration of initial participants, all tracking

electronic– 99K registered, 24K initiated chains, 384 reached targets

• Some findings:– < 5% of messages through any penultimate individual– large “friend degree” rarely (< 10%) cited– Dodds et al: no evidence of connectors!

• (but could be that connectors are not cited for this reason…)

– interesting analysis of reasons for forwarding– interesting analysis of navigation method vs. chain length

Agenda: Tuesday, Feb 1

• In-class Lifester network experiment• Finishing up Gladwell• Start on graph theory

Navigation in Social Networks:

A Controlled Experiment

diameter:worst-case: 5average: 2.86

Description of the Experiment• Participation is mandatory and for credit• If you don’t have your Lifester neighbor profiles, you cannot participate

– unless you have memorized your neighbor info• We will play two rounds• In each round, each of you will be the source of a navigation chain• You will be given a destination user to route a form to• Give the form to one of your Lifester neighbors who you think is “closer” to the

target• Write your Lifester UserID on forms you receive, and continue to forward them

towards their destinations• Points will be deducted for violations of the neighborhood structure• In one round, you will be given the Lifester profile of the destination• In the other round, you will not be given the destination profile• Then we’ll do some brief analysis with more detail to follow

The Strength of Weak Ties• Not all links are of equal importance• Granovetter 1974: study of job searches

– 56% found current job via a personal connection– of these, 16.7% saw their contact “often”– the rest saw their contact “occasionally” or “rarely”

• Your “closest” contacts might not be the most useful– similar backgrounds and experience– they may not know much more than you do– connectors derive power from a large fraction of weak ties

• Further evidence in Dodds et al. paper• T&M, Granovetter, Gladwell: multiple “spaces” &

“distances”– geographic, professional, social, recreational, political,…– we can reason about general principles without precise

measurement

Stickiness• Generalizes the notion of infectiousness• A common marketing term• How likely is the idea, fashion, etc. to be transmitted?• Can also view as the “failure probability” of a link• Some examples:

– “Winston tastes good…”– Columbia Record Club Gold Box– Sesame Street and Blues Clues

• In modern times, stickiness may trump raw exposure– supplementary readings on “viral” and “word-of-mouth”

marketing

• Persuasion (messenger) and stickiness (message) related• Making technology sticky:

– “The Media Equation”, by Nass and Reeves– human reaction to technology design and interface

The Power of Context• Transmission on a network (social or otherwise) can

be modulated by subtle changes in global influences– heat waves: crime, the power grid, and Amtrak

• Broken Windows and the NYC squeegee crackdown• Gladwell: “…the premise that an epidemic can be

reversed, can be tipped, by tinkering with the smallest details of the immediate environment.”

• Human behavior strongly and subtly influenced by context

• The Stanford Prison Experiment • The Good Samaritans of Princeton

The Magic Number 150

• Social channel capacity– correlation between

neocortex size and group size– Dunbar’s equation: neocortex

ratio group size

• Clear implications for many kinds of social networks

• Again, a topological constraint on typical degree

• From primates to military units to Gore-Tex

• Next up: let’s make some of these ideas more precise– graph theory: the mathematical language of networks– social network theory