Social Networks. Lecture outline. General overview Illustrations of types of networks Basic concepts for thinking about networks Implication of structural properties of networks Triadic close & friendship formation Structural holes & power Small worlds & diffusion.
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Size of personal networks
Strong ties: 6-30
Weak ties: ~150 persons with interaction
V. Weak ties: >1000 persons recognized
Networks generally sparse
Most of one’s ties don’t know each other
Networks exhibit small worlds (i.e., most nodes linked via a few hops)
Ties are specialized
Exchange different resources with different ties (e.g., friendship & work)
Only weak correlations among exchanges within a tie (e.g., correlations between communication frequency across modalities=~.3 to. 4)
Strong ties useful for
Weak ties useful for
Dense networks are good for the group as a whole
Structural holes provide opportunities for competitive advantage
Similar people tend to form ties
Friends of friends tend to form ties
Holes fill in
Useful for Organizational Diagnosis
Moody, James (2002) Race, School Integration, and Friendship Segregation in America. The American journal of sociology [0002-9602] Moody yr:2002 vol:107 iss:3 pg:679
Adamic, L. A., & Glance, N. (2005). The political blogosphere and the 2004 US election: divided they blog LinkKDD '05 Proceedings of the 3rd international workshop on Link discovery (pp. 36-43). NY: ACM.
Direct links between nodes
Represented by an N actor X N actor data matrix
Tangible exchange/Material support
Indirect links between nodes joined because they participate in a common group or event
Represented by N (actor) X M (group) matrix
Attends a common event
Edits the same Wikipedia page
Member of corporate board
Gives to same organization
Kossinets, G., Kleinberg, J., & Watts, D. (2008). The structure of information pathways in a social communication network KDD '08 Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 435-443): ACM.
Which Village Is More Likely to Survive?
Small world phenomenon:
Milgram’s& Travis(1969) experiment
Given a target individual (stockbroker in Boston), pass the message to a person you correspond with who is “closest” to the target.
Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry, 32(4), 425-443.
“Six degrees of separation”
20% of initiated chains reached target
average chain length = 6.5
~ 4-6 intermediaries
Connections thru target’s professional circle tended to be more direct; connections thru hometown take longer.
Small World Project - Columbia University
The Electronic Small World Project
Small World – 2002 Replication
Dodds, Muhamad, Watts,
Science 301, (2003)
Source: NASA, U.S. Government; http://visibleearth.nasa.gov/view_rec.php?id=2429
Ideal chain length btw 5 & 7
Chains more likely to complete
Target & sender in same country
Target & sender same gender
Pass through professional ties
Chains start w/in country then move to occupation
Going thru hubs doesn’t help
Number at Length L
Histogram of chain length by country of initial sender & target (assuming random attrition of 63%/link)
Introduced a family of “small world” networks with small diameter.
Regular ‘local’ links, with some random ‘long’ links
Local links ~ strong ties, provide clustering
Long links ~ weak ties, provide links among clusters
Local links are like towns
Long links connect the towns
Considered the problem of efficient decentralized routing in small world graphs.
How do people know how to efficiently get a message to someone they don’t even know?
Proved that in Watts & Strogatz’s model there is no decentralized algorithm that finds short paths between nodes.
Defined his own model of ‘small world’ graphs where short paths can be found in a decentralized way.
His model arranged nodes along lattice points.
Each node is connected to all its neighbors.
Also, a single random long link is chosen.
The probability that v is chosen is proportional to (1/r)a where r is the distance to v and a is some constant.
Showed that the only time that there exists a decentralized algorithm that finds short paths in his model is when a=2.
Algorithm: The Greedy Approach
What does this mean in the real world?
Does this mean Kleinberg’s model is exactly how the world works?
Models are toys that help us understand the real world!
This should be viewed sort of like a proof of concept.
The results of Milgram’s experiment should not be viewed as some sort of fluke or chance occurrence, but rather the result of some interesting underlying structural phenomena.
S-shaped diffusion curve
Shape differs across innovations: speed & asymptote
Phone: 60 years to reach 50% household penetration & asymptotes at 93%
Radio: 10 years to reach 50% household penetration & asymptotes at 99%
TV: 9 years to reach 50% household penetration & asymptotes at 98%
VCR: 6 years to reach 50% household penetration & asymptotes at 84%
Connected people are likely to share similar body mass indices.
Not simply self-selection
Chances of becoming obese increased by 57% if person has a friend who became obese in a given interval
Chances of becoming obese increased by 40% one’s adult sibling became obese
Yellow circles == obese; green non-obese. Purple link = friendship or marriage tie; Orange=familial tie
Christakis and Fowler (2007) The Spread of Obesity in a Large Social Network. The New England Journal of Medicine