Reading Group “Networks, Crowds and Markets” Session 1: Graph Theory and Social Networks Typ hier de naam van de FEB afzender

Overview Introduction Reading Group Ch. 2 Graphs, Paths and Small Worlds Ch. 3 Strength of Weak Ties Ch. 4 Homophily  Schelling model Typ hier de footer2

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 Typ hier de footer3

Introduction to the Reading Group Additional comments  Treated chapters are in Syllabus  Chapters are online:  book/ book/  Book is at Undergraduate level  Consider Advanced Material and additional papers when presenting Typ hier de footer4

GRAPHS, PATHS AND SMALL WORLDS Chapter 2 Typ hier de footer5

A social network Typ hier de footer6

A financial network Typ hier de footer7

A technological network: ARPANET Typ hier de footer8

Graphs, Paths and Distances A network is mathematically represented by a graph, G=, a set of vertices (nodes) V and the edges (ties, links) between them A graph can be directed or undirected Typ hier de footer9

Graphs, Paths and Distances A path is a sequence of (distinct) nodes, v 1, v 2, …, v k, such that for each i in {1,…,k-1} there is an edge between v i and v i+1 Typ hier de footer10 GJHML is a path

Graphs, Paths and Distances The distance between two nodes v 1 and v 2 is the length of the shortest path between them Typ hier de footer11 The shortest path between G and L is (among others) GJHL and its length is 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 Typ hier de footer12

Distribution of Chain Lengths Typ hier de footer13

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? Typ hier de footer14

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 Typ hier de footer15

STRENGTH OF WEAK TIES Chapter 3 Typ hier de footer16

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? Typ hier de footer17

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 Typ hier de footer18

Strength of Weak Ties 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 Typ hier de footer19 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 Typ hier de footer20 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 Typ hier de footer21 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. Strength of Weak Ties Typ hier de footer22 C B A D E F

Strength of Weak Ties 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) Typ hier de footer23

HOMOPHILY Chapter 4 Typ hier de footer24

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 Typ hier de footer25

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 Typ hier de footer26

Homophily at a U.S. High School Typ hier de footer27

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) Typ hier de footer28

Social-Affiliation Network Network of persons and social foci (activities) Typ hier de footer29

Triadic Closure Typ hier de footer30

Focal Closure Selection: Karate introduces Anna to Daniel Typ hier de footer31

Membership Closure Social Influence: Anna introduces Bob to Karate Typ hier de footer32

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 Typ hier de footer33

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 Typ hier de footer34

Homophily Measuring the mechanisms behind homophily is a hot topic  Kossinets & Watts (2006): Detailed course and interaction data from university  Centola (2010, 2011): Experimental data on social influence controlling network structure  Sacerdote: Social influence among students after randomized dorm assignment Typ hier de footer35

Homophily and Segregation Neighborhoods tend to be segregated according to race or culture  Ghetto formation  What is the mechanism behind that? Typ hier de footer36

Segregation in Chicago Typ hier de footer37

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 Typ hier de footer38

Schelling’s model (k=3) Typ hier de footer39 X

Schelling’s model (k=3) Typ hier de footer40 X

Schelling’s model online s/schelling/ Typ hier de footer41

Typ hier de footer42

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 Typ hier de footer43

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 Typ hier de footer44