Web Science Course Lecture: Social Networks - * Dr. Stefan Siersdorfer 1 * Figures from Easley and Kleinberg 2010 (

What is a Social Network ? Entities (persons, companies, organizations) Connections between entities (friendship, collaboration) 2

Examples of Social Networks „Real World“ relationships between people (friends, colleagues, relatives, …) Online Networks: Facebook, Flickr, Twitter … Trading Networks between companies or countries Collaborations and rivalries beween persons, organizations, and countries Extension: Technological Networks (WWW, Road Networks, Power Grids,...) 3

Example 1: Karate Club 4

Example 2: Communication in Organization (HP) 5

Example 3: Trade between Countries 6

Example 4: Medieval Trading in Europe 7

Example 5: World Wide Web (Blogs on Presidental Election in 2004) 8

Research Questions How do social networks form and how can we model the structure of Social Networks? How does information and innovation propagate in Social Networks? How do diseases propagate in Social Networks? How does trade and buisiness work in Social Networks? How to detect communities within Social Networks? …. 9

Topics of this Lecture Homophily and Segregation Friends and Foes The Small World Phenomenon 10

PART I: Homophily and Segregation 11

Properties of Nodes and Homophily Properties: age, gender, education, location, profession, political opinion, … Homophily: Similar nodes are more likely to form links. Reasons for homophily: – Selection of similar persons as contacts – Becoming more similar to contacts 12

Example: School Network 13

Segregation Example: Chicago 14

Segregation: Schelling Model (1) 15

Segregation: Schelling Model (2) 16

Segregation: Schelling Model (3) 17

Segregation: Schelling Model (4) 18

Segregation: Schelling Model (5) 19

Vacant slot Example: Linear Schelling (-like) Model

PART II: Friends and Foes 21

Positive and Negative Relationships Negative Relationships: – “Real Life”: people you don’t like, rivals, enemies – Online: Slashdot, Epinions – Economy: competitors – Countries: enemies

Structural Balance 23 Balanced Unbalanced

Structural Balance: Global Consequences 24

Weak Structural Balance In addition to triangles in Structural Balance: – Allow: triangles with 3 negative edges Global consequences: 25

Further Generalizations Incomplete networks: Structural Balance iff can be extended to complete balanced network by adding signed edges Approximate Balanced Networks: Balance property can be violated for fraction of triangles 26

International Relations (1) 27 USRR USA Pakistan India China North Vietnam

International Relations (2) 28

PART III: The Small World Phenomenon 29

Small World and „Six Degrees of Separation“ Small Word Phenomenon: Paths connecting two people in a social network are short (Pop Culture: „Six Degrees of Separation“) Milgram Experiment (1960s): – Ask set of „starters“ to forward a letter to „target“ person – „starters“ are given some information, e.g. address, occupation – Rule: forward letter to person‘s you know on a first-name basis 30

Milgram Experiment: Results 31

Small Wold: MS Instant Messenger 32

Modelling the Small World Phenomenon (1) 33

Model (2): Watts-Strogatz 34

Model (2): Watts-Strogatz contd. 35

Decentralized Search Watts-Strogatz model does not explain feasibility of decentralized search 36

Modelling Decentralized Search Idea: probability of random edge beteen nodes v and w decay with distance: ~ d(v,w) q 37

What‘s the best q for decentralized search? 38

Decentralized Search: Explaination 39

Generalization of Distance Decay: Rank Decay 40 Idea: probability of random edge beteen nodes v and w decay with rank of distance: ~ rank(w) p Optimal p: -1

Empirical Evidence: LiveJournal Experiment 41

Seminar Papers 42

Papers (1): Small World Phenomenon Jeffrey Travers, Stanley Milgram: An experimental study of the small world problem. Sociometry, 1969, 32(4): Jure Leskovec, Eric Horvitz: Planetary-scale views on a large instant-messaging network. WWW 2008:

Papers (2): Friends and Foes Jure Leskovec, Daniel Huttenlocher, Jon Kleinberg: Signed networks in social media. CHI 2010: Jérôme Kunegis, Andreas Lommatzsch, Christian Bauckhage: The slashdot zoo: mining a social network with negative edges. WWW 2009: