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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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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

What Are Social Networks?

  • Social network analysis – Graph-theory-based techniques for describing the topology of links between a set of people (or other objects)

  • Social and psychological theories – Theory about the causes and consequences of the social relationships revealed by social network analysis

  • Social networking sites – Internet sites based on displaying & exploiting explicit links between memberse.g., Facebook, MySpace, LinkedIn, Friendster

Structural View

  • The set of (exchange) relationships between people or other social units.

  • A graph, with people, groups, or organizations as the nodes and the entities exchanged as the link

  • Vary in size, density, clumpiness

  • Structure matters

  • Clique

  • Isolates

  • Stars

  • Boundary spanners

Why are they important?

  • Examining social networks can help diagnose social structures: Problems & opportunities

    • Find most important actors

    • Select successful team leaders and managers

    • Find informational bottlenecks/distribution channels

  • Connected actors often influence each others’ behavior

    • Information flows

    • Flows of support

  • Structure is important: One’s position in a social network enables/constrains one’s options

Reading Structure

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



Arduous help


Weak ties useful for

New information

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

Some Stylized Facts

Useful for Organizational Diagnosis

Race & school friendships

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

79% non-Asian

83% Asian

Familiarity in a CMU Project Class

Links among political blogs, 2004

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.

Links among political websites, 2009

Basic Concepts

Representing relations as networks

1 mode:

Direct links between nodes

Represented by an N actor X N actor data matrix





Trust/social support

Tangible exchange/Material support






2 mode:

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

Types of Edges (Relationships)

Directed graph (e.g, who likes whom)

Undirected graph (e.g, who knows whom)

Basic Concepts

Granovetter: Strength of Weak Ties

  • ~ 50% of new jobs come thru social contacts

  • Strong tie = "close relationship/friend". Social relationship with high frequency, emotional commitment, multiplicity, and reciprocity

    • Strong ties tend to know same things & people

    • Strong ties tend to fill in the gaps (e.g., friends of friends become friends; friends tend to share taste)

  • Weak tie = "weak relationship/causal acquaintance". Social relationships with low frequency, intensity, breadth, and reciprocity

    • Hypothesis: Weak ties lead to more extensive and diverse social networks, and are more likely to overcome gaps of class, race, and other sources of division

    • Data: Job changers get their jobs through weak ties: only 16% from contacts they see weekly and 28% from contacts they see less than yearly

Strength of ties on FaceBook

Strength of ties

  • Strong ties (Krackhard)

    • Intimacy, self-disclosure, provide support

    • Feel close w/frequent contact

    • Spouse, relatives, close friends

  • Weak ties (Granovetter)

    • Diverse resources, broader base

    • Feel distance w/infrequent contact

    • Acquaintances, colleagues from elsewhere

Homophily, transitivity, and bridging

Triadic Closure

  • Unconnected nodes connected to common nodes are likely to form connections

  • More likely to occur when their connections to the common node are strong

Balance theory & triadic closure(Heider, ’58; Newcomb, ’61)

  • Similar people form ties

  • Given a dyad of actors, ties tend to be reciprocated

  • Triadic closure: Given a triad of actors A, B and C,if A is strongly tied to B and to C, it is likely B and C will be at least weakly tied

  • The tendency to resolve unbalanced triads strongest when ties are affective

Strength of ties & likelihood of closure

Tie formation in an email network based on common friends

  • Linearity: Probability of ties formation increases with number of mutual ties already formed

  • Superlinearity: Having at least 2 mutual ties is especially important

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.

Closure & Joining: Friendster

  • Linearity: Probability of ties formation increases with number of mutual ties already formed

  • Superlinearity: Having at least 2 mutual ties is especially important

Closure & Joining: Wikipedia

Thinking about key nodes: Degree Centrality

Paths and shortest paths

Betweenness Centrality

  • Betweeness coded by hue:

    • Reds  low betweeness centrality

    • Blues  high betweenness

Eigenvector Centrality

Interpreting Centrality Measures


Stunning Density ComparisonHow well do you know other students in your major?



Who Helps Whom with the Rice Harvest?

Which Village Is More Likely to Survive?


Structural holes

  • A structural hole exists when there is only a weak connection between two dense clusters

    • Control benefits:

      • brokers control the interaction between two network components

    • Information benefits:

      • brokers have access to unique information, this makes them invaluable

  • Structural holes provide a competitive advantage

    • Separate non-redundant sources of information

    • Information from different sources is more additive than overlapping

Structural Holes (II)

Advantages of Structural Holes (Burt, 2000)

Small Worlds

Small Worlds and 6 Degrees of Separation

  • Small World Hypothesis: Everyone in the world can be reached through a short chain of social ties.

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.



Small world phenomenon:Milgram’s experiment

“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 – Results

  • Common channels:

    • 16 (25%) reached the target through the same neighbor

    • 10 reached the target through one business associate, 5 through another

  • Nearly 50% of the letters reached the target through same three people!

    • “social stars” – high degree and betweenness centrality!

Small World Project - Columbia University

The Electronic Small World Project

Small World – 2002 Replication

email experiment

Dodds, Muhamad, Watts,

Science 301, (2003)

  • 18 targets

  • 13 different countries

  • 60,000+ participants

  • 24,163 message chains

  • 384 reached their targets

  • average path length 4.0

Source: NASA, U.S. Government;

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

Attributions of completions

  • Average attrition of 63% at each link  only 384 chains complete (1.5%)

    • This is much larger than chance (.25%)

      • .

    • This is much worse than original Milgram (22%)



Number at Length L



Histogram of chain length by country of initial sender & target (assuming random attrition of 63%/link)

Watts & Strogatz (1998): Collective Dynamics of ‘Small-World’ Networks

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

Kleinberg (1999): The Small-World Phenomenon: An Algorithmic Perspective

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.

Kleinberg (1999): The Small-World Phenomenon: An Algorithmic Perspective

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

Kleinberg (1999): The Small-World Phenomenon: An Algorithmic Perspective

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.

Social Networks Are Major Route Through Which Social Influence Happens

  • Diffusion of innovation

  • Health & Happiness

  • Friendship formation

  • Trust

  • Spread of information

    • Small world phenomenon

Diffusion of innovation follows a predictable course

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

Spread of Obesity

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

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