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 GrowthExponential 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 WebWeb 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 ProjectInternet 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.” SOURCE: <http://research.lumeta.com/ches/map>

“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.”

Mapping Major ISPsThis 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.” <http://www.iprcom.com/papers/pagerank/>

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:

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

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-fociTransitory, 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

Netville WiredCase 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 1519

25

10 90

29

86

48

2836

63

128

35

17

71

88

47

17

7 6 87660

20

40

60

80

100

120

140

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)

345

72 83

5 6 9

236

194192207

248

11097102109

136 124

7687106 92

3619

1

120

975

650

50

100

150

200

250

300

350

400

Never Rarely Monthly Weekly Few times/wk Daily

Email Use

Total Phone F2F Email 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 communities

Hampton, Keith and Barry Wellman. 2003. “Neighboring in Netville.” City & Community 2(4):277-311.

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.

References