Small World Dynamics and Internet-Social Network Analysis Theories and Analysis-Lecture-Sociology, Lecture notes for Social Networks Theory and Analysis. Minnesota State University (MN)

Small World Dynamics and Internet-Social Network Analysis Theories and Analysis-Lecture-Sociology, Lecture notes for Social Networks Theory and Analysis. Minnesota State University (MN)

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“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” involvi...
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SOC 8311 Basic Social Statistics


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 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

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 <>

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,

Shop, Office


Work, Unit,







Groups Home Bases

Network of




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” < event/wellman%20workshop.ppt>


• 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

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 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


10 9





28 36





7 1


4 7


7 6 876 60








Never Rarely Monthly Weekly Few times/ wk Daily

Email Use

Total Phone F2F Email Letters

Figure 3a: Frequency of Contact with Near-By Friends (Days/Year)


72 83

5 6 9


194192 207



136 124

7687 106 92

36 19



9 75

65 0









Never Rarely Monthly Weekly Few times/wk Daily

Email Use

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

work relationships

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.


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