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SMALL WORLD DYNAMICS & INTERNET
Milgram‟s (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.... 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. It‟s a profound thought.... How every person is a new
door, opening to other worlds.”
John Guare. 1990. Six Degrees of Separation. New York: Vintage.
“It‟s 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.
Distances to Target for 3 Sending Groups
SOURCE: James Moody 2007
Bawl ’n Chain
SOURCE: James Moody 2007
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?
Watts Up, Doc?
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.
In a huge (billions), sparse (<<.001%), decentralized (no stars), and
clustered (cliques) network, small changes can transform substantially.
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.
Are You a Cavemen or a Solarian?
Connected caveman is most clustered small world. But, on Solaria in
Isaac Asimov‟s 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 α = 0
Solarians α = ∞
α = 1
Tunable parameter α
governs propensity to
meet or become friends:
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?
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
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
Internet is a packet-switching network.
Packet is a data unit created by TCP
software for transmission using domain
names and Internet Protocol addresses.
Exponential growth of Internet hosts took off in late-1990s. By Sept.
2007, more than 1.2 billion people had connections to the Web.
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.
A Geographic Internet Map
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?
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.
SOURCE: Internet Domain Survey July 1999 <http://mappa.mundi.net/maps/maps_007/>
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.
Internet map published in Wired (1998), for 100,000 nodes based on “half
a dozen simple rules, simulating various springs and repelling forces.”
“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
Mapping Major ISPs
This Internet map has a diameter of ~10,000 „pookies‟ (an arbitrary distance unit)
How to Become Very Popular on Google
Google‟s hypertext search software, PageRank™, for ranking
Webpages using link structures to indicate individual page
values. Google treats page A‟s citation of page B as a “vote”
by page A for page B. But, Google also takes into account A‟s
page rank. Votes cast by “important” pages count more
heavily, helping make other pages more “important.”
More generally, weighted-status methods calculate an ego‟s
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.”
By 2002, about 95% of browsing used Microsoft‟s Internet Explorer,
but 75% of external referrals on most Websites were from Google.
The Internet in Everyday Life
“Cyberspace” is the social counterpart to the Internet‟s 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 people‟s use of the Internet?
Three Interaction Modes
Phenomena Little Boxes:
Metaphor Fishbowl Core-
Unit of Analysis Village, Band,
Groups Home Bases
Era Traditional Contemporary Emerging
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)?
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
Barry Wellman. “Netting Together” <www.ksg.harvard.edu/digitalcenter/ event/wellman%20workshop.ppt>
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
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 Canada‟s no-cost Internet
services. Keith Hampton‟s 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 > 500 km; (2) gave more
help: childcare, home repairs; (3) received help
from friends and relatives, especially 50 to 500 km.
Hampton & Wellman (2003)
Altho getting wired expectedly sustained more distant community
ties, it surprisingly also increased local face-to-face neighboring:
“The local becomes just another interest.”
Figure 5a: Frequency of Contact with Far-Away Friends (Days/Year)
19 17 15 19
7 6 876 60
Never Rarely Monthly Weekly Few times/ wk Daily
Total Phone F2F Email Letters
Figure 3a: Frequency of Contact with Near-By Friends (Days/Year)
5 6 9
7687 106 92
Never Rarely Monthly Weekly Few times/wk Daily
Total Phone F2F Em ail Letters
Conclusion: Community Transformed
Partial communities comprised of
shared, specialized interests
Networked society is both more
uncertain & more maneuverable –
for people with the tools & skills
o Connectivity changes by all available means - door-to-door,
place-to-place, and person-to-person
o Less-solidary households, and more networked & virtual
o New forms of community, partial memberships in multiple
Hampton, Keith and Barry Wellman. 2003. “Neighboring in Netville.” City & Community
Milgram, Stanley. 1967. “The Small World Problem.” Psychology Today 2:60-67.
Travers, Jeffrey and Stanley Milgram. 1969. “An Experimental Study of the Small World
Problem.” Sociometry 32:425-443.
Watts, Duncan and Steven Strogatz. 1998. “Collective Dynamics of „Small-World‟ Networks.”
Nature June 4:440-442.