SMALL WORLD DYNAMICS

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SMALL WORLD DYNAMICS INTERNET
Its a small world after all and Kevin Bacon
Game exemplify the natural-network experiment of
Stanley Milgram, a social psychologist best known
for his controversial Behavioral Study of
Obedience to Authority involving administration
of electric shocks.
Milgrams (1967) less-notorious experiment
explored how few first-name intermediaries were
needed to deliver letters from 200 people in
Omaha and 100 in Boston to Sharon, a Boston
stockbroker. The unexpected average was six steps
(paths), hence the title of this play/movie
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.... Its not just the big names. Its
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. Its a profound
thought.... How every person is a new door,
opening to other worlds. John Guare. 1990. Six
Degrees of Separation. New York Vintage.
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Distances to Target for 3 Sending Groups
SOURCE James Moody 2007
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Bawl n Chain
Most successful chains needed just a few
intermediaries to reach the target, converging on
alters toward the end of each path. But, 78 of
96 nonstockbrokers in Nebraska failed to
complete! So is six degrees empirically bogus?
SOURCE James Moody 2007
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Watts Up, Doc?
In a huge (billions), sparse (ltlt.001),
decentralized (no stars), and clustered (cliques)
network, small changes can transform
substantially.
Duncan Watts and Steven Strogatz (1998) proposed
a universal class of small-world network models,
where clustering (C high local density) and
average shortest path length (L separation) are
a function of p the fraction of randomly
rewired links.
To a fully connected lattice network, start
adding a few long-distance connections to
destinations chosen uniformly at random.
Resulting network has local clustering short
paths, like many real world nets. A small world
network is any graph with a relatively small L
high C.
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Are You a Cavemen or a Solarian?
Connected caveman is most clustered small world.
But, on Solaria in Isaac Asimovs Naked Sun,
people live solitary lives on vast estates and
only interact virtually with one another
(including their spouses).
Even a single common friend implies two cavemen
are likely to meet, while all Solarian
interactions are equally unlikely, regardless of
how many friends they have in common.
Cavemen a 0
a 1
Tunable parameter a governs propensity to meet or
become friends
Solarians a 8
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The New Science of Networks
The simple small world network occupies a broad
region of p values where clustering C(p) is high
relative to its random limit C(1), yet the
average path length among actors L(p) is as
small as possible.
Watts-Strogatz model predicts that numerous very
large real-world networks exhibit these
small-world features. Analyses of a movie-actor
affiliation network (the Kevin Bacon Game), the
Western U.S. power transmission grid, and even
nematode neural networks all satisfied the
small-world criteria.
Watts Strogatz model with parameter p randomly
rewired for 1,000 actors connected to 10 nearest
neighbors
Can generalizations from small-world models
explain empirical collective dynamics the speed
of infectious epidemics (Ebola, Internet
viruses), fashion crazes (Dutch tulips), even
purchases of Amazon.com books?
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The Internet Invented by Al Gore?

• Communication technology of Internet followed
  S-shape diffusion curve
• 1968 DARPA creates ARPAnet for defense
  contractors
• 1970 Five nodes Stanford, ULCA, UCSB, Utah, BBN
• 1974 Transfer Control Protocol (TCP)
  specification
• 1984 Internet with 1,000 host computers converts
  to TCP/IP

Internet is a packet-switching network. Packet
is a data unit created by TCP software for
transmission using domain names and Internet
Protocol addresses.
File to be transmitted is split into many small
packets, each assigned a number, containing
information about its content and
destination Packet data streams travel via
network-of-networks (server computers or
hosts), following different paths, and may be
repackaged enroute At destination, original file
reassembled from packets for reading/viewing
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Exponential Growth
Exponential growth of Internet hosts took off in
late-1990s. By Sept. 2007, more than 1.2 billion
people had connections to the Web.
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The World Wide Web
Web browsers emerged by the 1990s for finding and
downloading Webpages, data, documents,
multimedia.
Tim Berners-Lee is credited as inventor of the
World Wide Web in 1989 at the CERN European
Particle Physics Lab, clinking HyperText Markup
Language (HTML) to the Internet. He directs the
W3 Consortium, which is now seeking to create the
Semantic Web extension.
Commercial firms that market directories search
engines cover only a small percentage of all Web
content. But, researchers can use data from
their site- and page-links to visualize social
structures of the Internet and Web as network
diagrams.
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A Geographic Internet Map
John Quarterman mapped geographic locations of
Internet hosts as symbols on a world map (The
Matrix Computer Networks and Conferencing
Systems Worldwide. 1990. Digital Press). Count N
of hosts in major cities and countries, then plot
on world map as colored circles proportional to
size.
Note super-clusters in North America (purple
circle 1 million hosts) and Europe
(predominantly blue circles). What evidence do
you perceive of North-South digital divide
paralleling their economies?
SOURCE Internet Domain Survey July 1999
lthttp//mappa.mundi.net/maps/maps_007/gt
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The Internet Mapping Project
Internet Mapping Project started at Bell Labs in
1998, spun-off to Lumeta Corp in 2000. Map shows
frequent trace-route-style path probes, one to
each registered Internet entity. Objectives
acquire, save topological data over long period,
to analyze routing problems, service-denial
attacks, and graph theory.
The early results looked like a peacock smashed
into a windshield. We have no interest in the
specific endpoints or network services on those
endpoints, just the topology of the center of
the Internet. The database should help show how
the Internet grows. We think we can even make a
movie of this growth someday.
Internet map published in Wired (1998), for
100,000 nodes based on half a dozen simple
rules, simulating various springs and repelling
forces.
SOURCE
lthttp//research.lumeta.com/ches/mapgt
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Mapping Major ISPs
This Internet map has a diameter of 10,000
pookies (an arbitrary distance unit)
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How to Become Very Popular on Google
By 2002, about 95 of browsing used Microsofts
Internet Explorer, but 75 of external referrals
on most Websites were from Google.
Googles hypertext search software, PageRank,
for ranking Webpages using link structures to
indicate individual page values. Google treats
page As citation of page B as a vote by page A
for page B. But, Google also takes into account
As page rank. Votes cast by important pages
count more heavily, helping make other pages more
important. More generally, weighted-status
methods calculate an egos power within a network
as a function of all its alters powers.
We assume page A has pages T1...Tn which point
to it (i.e., are citations)C(A) is defined as
the number of links going out of page A. The
PageRank of page A is PR(A) (1-d) d
(PR(T1)/C(T1) ... PR(Tn)/C(Tn)) Note that
the PageRanks form a probability distribution
over web pages, so the sum of all web pages'
PageRanks will be one. PageRank or PR(A) can be
calculated using a simple iterative algorithm,
and corresponds to the principal eigenvector of
the normalized link matrix of the web. Ian
Rogers. The Google PageRank Algorithm and How It
Works. lthttp//www.iprcom.com/papers/pagerank/gt
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The Internet in Everyday Life
Cyberspace is the social counterpart to the
Internets physical technologies. Social network
researchers examine how Internet users adapt
their ties to its constraints and vice versa.
Barry Wellman asked The Community Question How
do large-scale divisions of labor affect and
are affected by smaller-scale community of kith
and kin? How have the Internet and communities
mutually shaped and transformed one another?
How is the Internet being incorporated into
everyday life? Does the Internet multiply,
decrease, add to - other forms of
communication? - overall communication? How is
the structure of interpersonal relations
affected? How does everyday life affect peoples
use of the Internet?
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Three Interaction Modes
Are communities shifting from densely-knit
little boxes to glocalized nets
(sparsely-knit with clusters, linking households
locally globally) to networked individualism
(sparsely-knit, linking individuals with little
regard to space)?
Phenomena Little Boxes Door-to-Door Glocalization Place-to-Place Networked Individualism Person-to-Person
Metaphor Fishbowl Core-Periphery Switchboard
Unit of Analysis Village, Band, Shop, Office Household, Work, Unit, Multiple Networks Networked Individual
Social Organization Groups Home Bases Network of Networks Networked Individualism
Era Traditional Contemporary Emerging
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Rise of Networked Individualism
Society moving from relations bound up in groups
to a multiple network and networking society,
characterized by Longer-distance ties,
sparsely-knit, loosely-bounded,
multi-foci Transitory, weaker ties, less caring
for strangers alienation? Flexible networks are
major sources of social capital

• CHANGES DRIVING NETWORKED INDIVIDUALISM
• Transportation communication becoming more
  individualized
• Affordable, portable computerization allows
  greater personalization
• Multiple employers, sequentially and
  contemporaneous
• Separation of work and home as physical places
• Working away from workplace Telework, flextime,
  road warrior
• Dual careers multiple schedules to juggle

Barry Wellman. Netting Together
ltwww.ksg.harvard.edu/digitalcenter/
event/wellman20workshop.pptgt
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Netville Wired
Case study of Netville, a new planned suburb of
Toronto, offered clues about how the Internet
becomes embedded into everyday lives. Some
residents chose Bell Canadas no-cost Internet
services. Keith Hamptons field ethnography
complemented a survey about Netville residents
Internet usage and networking.
One year after moving in, wired Netville
residents had enhanced local ties expanded weak
ties. Compared to nonwired, wired people (1) had
more social contact, especially gt 500 km (2)
gave more help childcare, home repairs (3)
received help from friends and relatives,
especially 50 to 500 km.
Altho getting wired expectedly sustained more
distant community ties, it surprisingly also
increased local face-to-face neighboring The
local becomes just another interest.
Hampton Wellman (2003)
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Conclusion Community Transformed

• Connectivity changes by all available means -
  door-to-door, place-to-place, and
  person-to-person
• Less-solidary households, and more networked
  virtual work relationships
• New forms of community, partial memberships in
  multiple communities

Partial communities comprised of shared,
specialized interests Networked society is both
more uncertain more maneuverable for people
with the tools skills
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References
Hampton, Keith and Barry Wellman. 2003.
Neighboring in Netville. City Community
2(4)277-311. Milgram, Stanley. 1967. The Small
World Problem. Psychology Today
260-67. Travers, Jeffrey and Stanley Milgram.
1969. An Experimental Study of the Small World
Problem. Sociometry 32425-443. Watts, Duncan
and Steven Strogatz. 1998. Collective Dynamics
of Small-World Networks. Nature June 4440-442.