Topics In Social Computing (67810) Module 1 Introduction & The Structure of Social Networks

The small world phenomenon People who do not know each other are often surprised to learn they have a mutual acquaintance “What a small world!” “What are the odds?” 2

What are the odds? Class Experiment Find a partner in the class: someone you do not know well. Try to find a mutual acquaintance of each type: – One in this room – One in HUJI (but not in this room) – One not in HUJI Before we start: How many pairs do you expect to see succeed? 3

A Naïve Model v u You Someone you don’t know The rest of the world 4

What are the odds? 5

Questions What is N? What is d? So what are the odds? What about triadic closure? Does it bias the results? Which way? You Someone you don’t know The rest of the world 6

Stanley Milgram’s “Six Degrees of Separation” In 1967 Stanley Milgram set out to test the small world phenomenon. – Milgram is also well known for his “obedience” experiments Instead of looking for a shared acquaintance, he looks for longer connecting chains between individuals. What is the length of the path that is needed to connect two “arbitrary” individuals? 7

Why does distance matter? Short average distance implies that ideas, innovation and other forms of cultural influence could spread quickly. Contrast with isolated civilizations where customs / culture / language became radically different over time 8

Six Degrees of Separation The Experiment: Milgram Recruits test subjects using ads in the paper. – e.g., subjects in Nebraska & Kansas. Subjects are asked to deliver a package to a stockbroker in Boston. Packages sent through “acquaintances” that should be closer to the target (like a chain letter) Tracer postcards are sent back in the mail from each intermediary 9

Milgram finds: Successful chains have 5-6 steps on average. “The Small World Problem” Milgram, Psych. Today, vol 1, no 1, pp Out of 160 chains. most chains did not complete 10

Erdos number: – Distance from Paul Erdos – Graph: edges are between people who published papers together Kevin Bacon number – Distance from Kevin Bacon – Graph: edges between actors that were in a movie together 11

Should we really be surprised? 12

Critique of Milgram’s experiment 1.Source individuals were not random – (people responding to add could be more “open” than average guy and have more social connections) 2.Neither was the target (a prominent individual) 3.The U.S. is not the whole world 4.Most packages did not reach destination – Longer paths have lower probability of success – biasing the results towards shorter paths 5.There is a difference between having a short chain and a finding one greedily – (so Milgram only provides an upper bound) 13

Followup studies address criticism study similar to Milgram’s study – 60,000 users worldwide – easier for participants than snail-mail Successful chains took ~4 steps When accounting for attrition: – 5 steps between people in same country – 7 steps between people in different countries Dodds, Muhamad, Watts. "An experimental study of search in global social networks." science (2003):

Facebook study covering ~720 million accounts Estimates: little over 4 degrees of separation – Does this without greedy routing How do you estimate the avg. distance in such a huge graph? You have to be really clever! See the paper: “Four Degrees of Separation” Backstrom et. al., arXiv: (2011) 15

Small World Networks 16 i kk

Small World Networks 17 Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature (1998):

Small World Networks Watts & Strogatz show via simulation that for some range of the parameter p, clustering can be high, and average path length can be low. 18 Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature (1998):

Greedy routing So why did greedy routing work? How are people able to get closer to the target at each step without a global view of the network? “The Small World Problem” Milgram, Psych. Today, vol 1, no 1, pp

Kleinberg’s Model Greedy Routing on a Small World Network (See Lecture Notes) 20

Greedy routing Kleinberg’s model for greedy routing is geographically motivated. Is that how people actually route? Does link probability decay with distance? 21

Supporting Empirical Evidence A recent study examines the friendship network in LiveJournal. Some users have specified their geographic location. Problem: distribution of nodes is not uniform in 2D space (as Kleinberg assumed) 22 Liben-Nowell et al. "Geographic routing in social networks." PNAS (2005):

LiveJournal Study 23 Liben-Nowell et al. "Geographic routing in social networks." PNAS (2005):