The Tipping Point and the Networked Nature of Society

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The Tipping Point and the Networked Nature of
Society

• Michael Kearns
• Computer and Information Science
• Penn Reading Project 2004

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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.
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The Networked Nature of Society
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International Trade
KrempelPleumper
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Corporate Partnerships
Krebs
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Gnutella
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Internet Routers
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Artist Mark Lombardi
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An Emerging Science
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An Emerging Science

• Examining apparent similarities between many
  human and technological systems organizations
• Importance of network effects in such systems
• How things are connected matters greatly
• Structure, asymmetry and heterogeneity
• Details of interaction matter greatly
• The metaphor of viral spread
• Qualitative and quantitative can be very subtle
• A revolution of
• measurement
• theory
• breadth of vision

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Whos Doing All This?

• Computer Scientists
• Understand and design complex, distributed
  networks
• View competitive decentralized systems as
  economies
• Social Scientists, Psychologists, Economists
• Understand human behavior in simple settings
• Revised views of economic rationality in humans
• Theories and measurement of social networks
• Physicists and Mathematicians
• Interest and methods in complex systems
• Theories of macroscopic behavior (phase
  transitions)
• All parties are interacting and collaborating

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Real World Social Networks

• Example Acquaintanceship networks
• vertices people in the world
• links have met in person and know last names
• hard to measure
• lets do our own Gladwell estimate
• Example scientific collaboration
• vertices math and computer science researchers
• links between coauthors on a published paper
• Erdos numbers distance to Paul Erdos
• Erdos was definitely a hub or connector had 507
  coauthors
• MKs Erdos number is 3, via Mansour ? Alon ?
  Erdos
• how do we navigate in such networks?

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Update MKs Friendster NW, 1/19/03

• If you didnt get my email invite, let me know
• send mail to mkearns_at_cis.upenn.edu
• Number of friends (direct links) 8
• NW size (lt 4 hops) 29,901
• 134 29,000
• But lets look at the degree distribution
• So a random connectivity pattern is not a good
  fit
• What is???
• Another interesting online social NW thanks
  Albert Ip!
• AOL IM Buddyzoo

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Biological Networks

• Example the human brain
• vertices neuronal cells
• links axons connecting cells
• links carry action potentials
• computation threshold behavior
• N 100 billion
• typical degree sqrt(N)
• well return to this in a moment

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Universality and Generative Models
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A Canonical Natural Network has

• Few connected components
• often only 1 or a small number independent of
  network size
• Small diameter
• often a constant independent of network size
  (like 6)
• or perhaps growing only logarithmically with
  network size
• typically exclude infinite distances
• A high degree of clustering
• considerably more so than for a random network
• in tension with small diameter
• A heavy-tailed degree distribution
• a small but reliable number of high-degree
  vertices
• quantifies Gladwells connectors
• often of power law form

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Some Models of Network Generation

• Random graphs (Erdos-Renyi models)
• gives few components and small diameter
• does not give high clustering and heavy-tailed
  degree distributions
• is the mathematically most well-studied and
  understood model
• Watts-Strogatz and related models
• give few components, small diameter and high
  clustering
• does not give heavy-tailed degree distributions
• Preferential attachment
• gives few components, small diameter and
  heavy-tailed distribution
• does not give high clustering
• Hierarchical networks
• few components, small diameter, high clustering,
  heavy-tailed
• Affiliation networks
• models group-actor formation
• Nothing magic about any of the measures or
  models

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So Which Properties Tip?

• Just about all of them!
• The following properties all have threshold
  functions
• having a giant component
• being connected
• having a perfect matching (N even)
• having small diameter
• Demo look at the following progression
• giant component ? connectivity ? small diameter
• in graph process model (add one new edge at a
  time)
• example 1 example 2 example 3 example 4
  example 5
• With remarkable consistency (N 50)
• giant component 40 edges, connected 100,
  small diameter 180

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EpidemosThanks 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

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Incorporating Strategic and Economic Behavior
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Examples from Schelling and Beyond

• Going to the beach or not
• too few ? youll go, making it more crowded
• too many ? you wont go, or will leave if youre
  there
• Sending Christmas cards
• people send to those they expect will send to
  them
• everybody hates it, but no individual can break
  the cycle
• Investing in an apartment fire sprinkler
• only worth it if enough people do it
• insurance companies wont discount for it
• Choosing where to sit in the Levine Auditorium

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Local Preferences and Segregation

• Special case of preferences housing choices
• Imagine individuals who are either red or
  blue
• They live on in a grid world with 8 neighboring
  cells
• Neighboring cells either have another individual
  or are empty
• Individuals have preferences about demographics
  of their neighborhood
• Here is a very nice simulator

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A Sample Network and Equilibrium

• Solid edges
• exchange at equilibrium
• Dashed edges
• competitive but unused
• Dotted edges
• non-competitive prices
• Note price variation
• 0.33 to 2.00
• Degree alone does not determine price!
• e.g. B2 vs. B11
• e.g. S5 vs. S14

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The Internet as Society
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The Internet What is It?

• The Internet is a massive network of connected
  but decentralized computers
• Began as an experimental research NW of the DoD
  (ARPAnet) in the 1970s
• All aspects (protocols, services, hardware,
  software) evolved over many years
• Many individuals and organizations contributed
• Designed to be open, flexible, and general from
  the start
• Completely unlike prior centralized, managed NWs
• e.g. the ATT telephone switching network

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Hubs and Authorities

• Suppose we have a large collection of pages on
  some topic
• possibly the results of a standard web search
• Some of these pages are highly relevant, others
  not at all
• How could we automatically identify the important
  ones?
• Whats a good definition of importance?
• Kleinbergs idea there are two kinds of
  important pages
• authorities highly relevant pages
• hubs pages that point to lots of relevant pages
• (I had these backwards last time)
• If you buy this definition, it further stands to
  reason that
• a good hub should point to lots of good
  authorities
• a good authority should be pointed to by many
  good hubs
• this logic is, of course, circular
• We need some math and an algorithm to sort it out

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• Networked Life (CSE 112) web site
• www.cis.upenn.edu/mkearns/teaching/NetworkedLife
• these slides
• www.cis.upenn.edu/mkearns/teaching/NetworkedLife/
  prp.ppt
• Feel free to contact me at
• mkearns_at_cis.upenn.edu