CSCI 2350/INTD 2350: Social & Economic Networks What does a - - PDF document

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CSCI 2350/INTD 2350: Social & Economic Networks

Mohammad T . Irfan Email: mirfan@bowdoin.edu What does a real-world network look like? Reading: Ch 2 of EK, Ch 2 & 3 of Jackson

Networks and contagion

u Ebola epidemic December 2013 – present

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Real-World Networks

And their common properties

• 1. Macro-level
• 2. Micro-level

Macro-level properties

• 1. Giant components
• 2. Small-world effect
• 3. Degree distribution
• 4. Clustering

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• 1. Giant component

u Intuitive example u Actor network

u 98% of 449,913 actors belong to the giant

component (May 2000) u Other examples

u Instant messaging u Co-author network u Email u Biological networks (neural networks) u Technology networks (WWW, power grid)

What is the implication?

High school relationships (1993-95)

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• 2. Small-world effect

u Proposition

u The average shortest path between any two nodes

in a connected component is “small” u Intuition

Six degrees of separation

u Hungarian author Frigyes Karinthy (1929

short story “Chains”)

u John Guare’s play (1990) & later movie

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Milgram’s experiment (1963) Milgram’s experiment (cont…)

u Critiques…

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What is the implication

• f small-world?

“Six worlds apart?” Contagion of TB (Valdis Krebs, Oklahoma, 2002)

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Computational question

u How to find the “right 6 people?”

u Breadth-first search (BFS) algorithm to find the

shortest path u Fun application– Bacon number

u Bacon number of an actor = distance from Kevin

Bacon

u Average Bacon number: 2.9 u https://oracleofbacon.org/

Animal House Apollo 13 The Wild River Da Vinci Code Titanic Holiday Joe vs. Volcano High Noon Dial M for Murder The Eagle Has Landed Cold Mountain Hamlet Portrait of a Lady

Bill Paxton Tom Hanks Paul Herbert Yves Aubert Kate Winslet Kevin Bacon Meryl Streep Donald Sutherland John Belushi Kathleen Quinlan Lloyd Bridges Grace Kelly Patrick Allen Nicole Kidman John Gielgud

Charlie’s Angels

Bill Murray Cameron Diaz

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• 3. Degree distribution

u Power law distribution and scale-free

networks

• 4. Clustering coefficients

u Highly clustered

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Political blogs (2004) Micro-level properties

u Centrality

u Controversial topic

u 4 types

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Centrality measures

1.

Degree centrality

2.

Closeness centrality

3.

Betweenness centrality

4.

Prestige/eigenvector centrality

Review: Closeness centrality

u Centrality of node i =

1/average shortest path length from i to all

• ther nodes

u Q: How to compute closeness centrality?

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Centrality measures

1.

Degree centrality

2.

Closeness centrality

3.

Betweenness centrality

4.

Prestige/eigenvector centrality

Eigenvector centrality

u Tutorial on eigenvector

u Jackson’s Section 2.4 (Appendix) u http://www.mathportal.org/calculators/matrices-

calculators/matrix-calculator.php

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Comparison of centrality measures