Web Science Course 2014 - Lecture : Social Networks - *

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Web Science Course 2014- Lecture: Social Networks - *

Dr. Stefan Siersdorfer

* Figures from Easley and Kleinberg 2010 (http://www.cs.cornell.edu/home/kleinber/networks-book/)

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What is a Social Network ?

• Entities (persons, companies, organizations)• Connections between entities (friendship,

collaboration)

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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, ...)

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Example 1: Karate Club

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Example 2: Communication in Organization (HP)

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Example 3: Trade between Countries

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Example 4: Medieval Trading in Europe

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

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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? • ….

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Topics of this Lecture

• Homophily and Segregation• Friends and Foes• The Small World Phenomenon

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PART I: Homophily and Segregation

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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

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Example: School Network

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Segregation Example: Chicago

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Segregation: Schelling Model (1)

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Segregation: Schelling Model (2)

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Segregation: Schelling Model (3)

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Segregation: Schelling Model (4)

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Segregation: Schelling Model (5)

Vacant slot

Example: Linear Schelling (-like) Model

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PART II: Friends and Foes

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

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Structural BalanceBalanced Unbalanced

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Structural Balance: Global Consequences

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Weak Structural Balance• In addition to triangles in Structural Balance: – Allow: triangles with 3 negative edges

• Global consequences:

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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

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International Relations (1)

USRR

USA

Pakistan

India

China

North Vietnam

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International Relations (2)

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PART III: The Small World Phenomenon

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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

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Milgram Experiment: Results

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Small Wold: MS Instant Messenger

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Modelling the Small World Phenomenon (1)

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Model (2): Watts-Strogatz

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Model (2): Watts-Strogatz contd.

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Decentralized Search

• Watts-Strogatz model does not explain feasibility of decentralized search

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Modelling Decentralized Search• Idea: probability of random edge beteen

nodes v and w decay with distance: ~ d(v,w)q

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What‘s the best q for decentralized search?

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Decentralized Search: Explaination

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Generalization of Distance Decay: Rank Decay

Idea: probability of random edge beteen nodes v and w decay with rank of distance: ~ rank(w)p

Optimal p: -1

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Empirical Evidence: LiveJournal Experiment

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Seminar Papers

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Papers (1): Small World Phenomenon

• Jeffrey Travers, Stanley Milgram: An experimental study of the small world problem. Sociometry, 1969, 32(4): 425-443

• Jure Leskovec, Eric Horvitz: Planetary-scale views on a large instant-messaging network. WWW 2008: 915-924.

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Papers (2): Friends and Foes

• Jure Leskovec, Daniel Huttenlocher, Jon Kleinberg: Signed networks in social media. CHI 2010: 1361-1370.

• Jérôme Kunegis, Andreas Lommatzsch, Christian Bauckhage: The slashdot zoo: mining a social network with negative edges. WWW 2009: 741-750.