45graph - 4.5 Small World Phenomenon Introduction to...

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Unformatted text preview: 4.5 Small World Phenomenon Introduction to Programming in Java: An Interdisciplinary Approach Robert Sedgewick and Kevin Wayne Copyright 2008 November 9, 2008 9:39 AM 2 Small World Phenomenon Small world phenomenon. Six handshakes away from anyone. An experiment to quantify effect. [Stanley Milgram, 1960s] ! You are given personal info of another person. ! Goal: deliver message. ! Restriction: can only forward to someone you know by first name. ! Outcome: message delivered with average of 5 intermediaries. e.g., occupation and age Stanley Milgram Kevin Bacon 5 Applications of Small World Phenomenon Sociology applications. ! Looking for a job. ! Marketing products or ideas. ! Formation and spread of fame and fads. ! Train of thought followed in a conversation. ! Defining representative-ness of political bodies. ! Kevin Bacon game (movies, rock groups, facebook, etc.). Other applications. ! Electronic circuits. ! Synchronization of neurons. ! Analysis of World Wide Web. ! Design of electrical power grids. ! Modeling of protein interaction networks. ! Phase transitions in coupled Kuramoto oscillators. ! Spread of infectious diseases and computer viruses. ! Evolution of cooperation in multi-player iterated Prisoner's Dilemma. Reference. Duncan J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press, 1999. 6 Graph Data Type Application demands a new data type. ! Graph = data type that represents pairwise connections. ! Vertex = element. ! Edge = connection between two vertices. A B F I E H D C G vertex edge 7 Graph Applications communication graph telephones, computers vertices edges fiber optic cables circuits gates, registers, processors wires mechanical joints rods, beams, springs hydraulic reservoirs, pumping stations pipelines financial stocks, currency transactions transportation street intersections, airports highways, airway routes scheduling tasks precedence constraints software systems functions function calls internet web pages hyperlinks games board positions legal moves social relationship people, actors friendships, movie casts neural networks neurons synapses protein networks proteins protein-protein interactions chemical compounds molecules bonds 9 High School Dating Bearman, Moody, and Stovel, 2004 Image by Mark Newman 10 Corporate Email Communications Adamic and Adar, 2005 11 Power Transmission Grid of Western US 7 Graph Applications communication graph telephones, computers vertices edges fiber optic cables circuits gates, registers, processors wires mechanical joints rods, beams, springs hydraulic reservoirs, pumping stations pipelines financial stocks, currency transactions transportation street intersections, airports highways, airway routes scheduling tasks precedence constraints software systems functions function calls internet web pages hyperlinks games board positions legal moves social relationship people, actors friendships, movie casts neural networks neurons synapses...
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This note was uploaded on 12/16/2008 for the course COS 126 taught by Professor Douglasw.clark during the Fall '08 term at Princeton.

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45graph - 4.5 Small World Phenomenon Introduction to...

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