Reading Group “Networks, Crowds and Markets” Session 1: Graph Theory and Social Networks Typ...

Reading Group “Networks, Crowds and Markets”Session 1: Graph Theory and Social Networks

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Overview

Introduction Reading Group Ch. 2 Graphs, Paths and Small Worlds Ch. 3 Strength of Weak Ties Ch. 4 Homophily

Schelling model

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Introduction to the Reading Group

Book: Networks, Crowds and Markets Why this book?

Multidisciplinary and Comprehensive Networks: Jon Kleinberg, Computer Scientist

Crowds and Markets: David Easley: Economist

Up to date (2010)

Good Reputation


Introduction to the Reading Group Additional comments

Treated chapters are in Syllabus

Chapters are online: http://www.cs.cornell.edu/home/kleinber/networks-book/

Book is at Undergraduate level Consider Advanced Material and additional papers

when presenting


http://www.cs.cornell.edu/home/kleinber/networks-book/

GRAPHS, PATHS AND SMALL WORLDS

Chapter 2


A social network


A financial network


A technological network: ARPANET


Graphs, Paths and Distances

A network is mathematically represented by a graph, G=<V,E>, a set of vertices (nodes) V and the edges (ties, links) between them

A graph can be directed or undirected



A path is a sequence of (distinct) nodes, v1, v2, …, vk, such that for each i in {1,…,k-1} there is an edge between vi and vi+1


GJHML is a path


The distance between two nodes v1 and v2 is the length of the shortest path between them


The shortest pathbetween G and Lis (among others) GJHL and its lengthis 3

Small-World Phenomenon

When we look at large social network with thousands of nodes, we find that distances are generally quite short, often less than 10. This is called the Small-World phenomenon

Stanley Milgram e.a. in 1960s: Small World Experiment

Random participants in Nebraska and Kansas were asked to

send a chain letter to Boston through first-name based

acquaintances


Distribution of Chain Lengths


Small Worlds

Milgram found that average lengths of the chains in the experiment was around six

Six degrees of separation This number has been replicated in other

studies, e.g. Leskovec & Horvitz in Microsoft Instant Messenger network

Why is this?


Small-World Phenomenon Suppose everyone has on average 100 acquaintances

and there is little overlap between acquaintanceships Me: 1

Acquaintances: 100

Acquaintances at distance 2: 100^2=10,000

Acquaintances at distance 3: 100^3=1,000,000

Acquaintances at distance 4: 100^4=100,000,000

Acquaintances at distance 5: 100^5=10,000,000,000


STRENGTH OF WEAK TIESChapter 3


Strength of Weak Ties

Links differ in terms of strength

Friends vs. Acquaintance Amount of contact time, affection, trust

Mark Granovetter (1974): Getting a Job Jobseekers obtain useful job info through social network

More often from acquaintances than from close friends

Why?


Strength of Weak Ties Granovetter (1973): The Strength of Weak Ties

Link between local network property and global

network structure Local: Triadic closure of triads with strong ties

Local-Global: Strong ties cannot be bridges

Global: Bridges more important for information transmission

Conclusion: Weak ties are more important for

information transmission



Triadic closure of triads with strong ties

A satisfies strong triadic closure property: for all B and C for which there is a strong tie AB and

AC, there is also a (strong or weak) tie BC


A

B

C

A

B

C

Strength of Weak Ties A bridge is a tie that connects two otherwise

unconnected components Information within group is often same

Information between groups is different

Bridge provides link to different information source,

and is therefore more important


C

B

A

D

E

F

Strength of Weak Ties Tie AB is a local bridge if A and B have no

friends in common

The span of a local bridge AB is the distance

between A and B after removal of AB itself


A B

AB is a local bridge of span 4

Claim: if a node A satisfies the Strong Triadic Closure and is involved in at least two strong ties, then any local bridge it is involved in must be a weak tie

Proof by contradiction: suppose C satisfies STC and CD is a strong bridge, then there is a triple BCD with BC and CD strong. But then, BD should be linked.



C

B

A

D

E

F


Empirical support for Strength of Weak Ties Theory

Onnela et al. (2007) Empirical support against Strength of Weak

Ties Theory

Van der Leij & Goyal (2011)


HOMOPHILYChapter 4


Homophily

Agents in a social network have other characteristics apart from their links

Non-mutable: race, gender, age

Mutable: place to live, occupation, activities,

opinions, beliefs Links and mutable characteristics co-evolve

over time


Homophily

When we take a snapshot in time, we observe that these node characteristics are correlated across links

E.g. Academics have often academic

friends, etc. This phenomenon that people are linked to

similar others is called homophily


Homophily at a U.S. High School


Homophily Mechanisms underlying Homophily

Selection A and B have similar characteristics -> A and B form a link AB

Social Influence A and B have a link -> B chooses the same (mutable)

characteristic as A

E.g. A starts smoking, and B follows (peer pressure)


Social-Affiliation Network Network of persons and social foci (activities)


Triadic Closure


Focal Closure Selection: Karate introduces Anna to Daniel


Membership Closure Social Influence: Anna introduces Bob to

Karate


Homophily Both Selection and Social Influence drive homophily How important is each mechanism?

Important question: Different mechanism implies

different policy, e.g. Policy to prevent teenagers from smoking

Social Influence. Target “key players” and let them positively

influence rest

Selection. Target on characteristics (e.g. family background) alone


Homophily Both Selection and Social Influence drive

homophily How important is each mechanism?

Difficult question: Requires longitudinal data

Requires observation of (almost) all characteristics

If a characteristic is not observed, then social influence

effect is overestimated


Homophily

Measuring the mechanisms behind homophily is a hot topic

Kossinets & Watts (2006): Detailed course and e-mail

interaction data from university

Centola (2010, 2011): Experimental data on social

influence controlling network structure

Sacerdote: Social influence among students after

randomized dorm assignment


Homophily and Segregation

Neighborhoods tend to be segregated according to race or culture

Ghetto formation

What is the mechanism behind that?


Segregation in Chicago


Homophily and Segregation

Segregation model of Thomas Schelling

Agent-based model Two different agents: X and O types

Agents live on a grid

weak satisficing preferences for homophily

At least k of the 8 neighbors of same type

Each period, agents who are not satisfied move to a

location where they are


Schelling’s model (k=3)


X

Schelling’s model online

http://cs.gmu.edu/~eclab/projects/mason/projects/schelling/




Schelling’s model

Surprising relation between micro-behavior and macro-outcomes

Weak satisficing preferences for homophily sufficient

to create complete segregation

Segregation arises due to miscoordination There exists an allocation involving complete integration

satisfying all agents, but individual decisionmaking does not

lead to that outcome


Overview Introduction Reading Group

Ch. 2 Graphs, Paths and Small Worlds

Ch. 3 Strength of Weak Ties

Ch. 4 Homophily

Schelling model

Planning

Next week: 6 March 13:00 Natasa Golo and Dan Braha

Next Reading Group: 13 March 13:30 h Maurice Koster: Ch. 8 and Ch. 10


Reading Group “Networks, Crowds and Markets” Session 1: Graph Theory and Social Networks Typ...

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