ICPSR - Complex Systems Models in the Social Sciences - Lecture 2 - Professor Daniel Martin Katz
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This document provides an overview of complex systems models in the social sciences, with a focus on network analysis. It introduces some key network concepts like nodes, edges, and the mathematical representation of relationships. It then discusses network analysis as an interdisciplinary field and provides examples of social, physical, biological, and computer science networks that have been studied. The document reviews some terminology and provides visual examples of networks. It also briefly outlines the history of network science, starting with Euler's work on the Königsberg bridge problem. Finally, it discusses some seminal network studies like Moreno's sociometry and Milgram's "six degrees of separation" small world experiment.
ICPSR - Complex Systems Models in the Social Sciences - Lecture 2 - Professor Daniel Martin Katz
- 1. Complex Systems Models in the Social Sciences (Lecture 2) daniel martin katz illinois institute of technology chicago kent college of law @computationaldanielmartinkatz.com computationallegalstudies.com
- 4. Introduction to Network Analysis What is a Network? What is a Social Network? Mathematical Representation of the Relationships Between Units such as Actors, Institutions, Software, etc. Special class of graph Involving Particular Units and Connections
- 5. Introduction to Network Analysis Interdisciplinary Enterprise Applied Math (Graph Theory, Matrix Algebra, etc.) Statistical Methods Social Science Physical and Biological Sciences Computer Science
- 6. Social Science For Images and Links to Underlying projects: http://jhfowler.ucsd.edu/ 3D HiDef SCOTUS Movie Co-Sponsorship in Congress Spread of Obesity Hiring and Placement of Political Science PhD’s
- 7. Social Science The 2004 Political Blogosphere (Adamic & Glance) High School Friendship (Moody) Roll Call Votes in Congress (Mucha, et al)
- 8. Physical and Biological Sciences For Images and Links to Underlying projects: http://www.visualcomplexity.com/vc/
- 9. Computer Science Mapping of the Code Networks are ways to represent dependancies between software
- 10. Computer Science Internet is one of the largest known and most important networks
- 14. Example: Nodes in an actor- based social Network Alice Bill Carrie David Ellen How Can We Represent The Relevant Social Relationships? Terminology & Examples
- 17. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
- 18. Alice Bill David Carrie Ellen A Full Representation of the Social Network Terminology & Examples
- 19. Bill David Carrie Ellen Terminology & Examples Alice A Full Representation of the Social Network (With Node Weighting)
- 20. Bill David Carrie Ellen A Full Representation of the Social Network (With Node Weighting and Edge Weighting) Terminology & Examples Alice
- 21. A Survey Based Example “Which of the above individuals do you consider a close friend?” Image We Surveyed 5 Actors: (1) Daniel, (2) Jennifer, (3) Josh, (4) Bill, (5) Larry
- 22. From an EdgeList to Matrix 1 2 3 4 5 --------------------------- Daniel (1) 0 1 1 1 1 Jennifer (2) 1 0 1 0 0 Josh (3) 0 1 0 1 1 Bill (4) 0 0 0 0 0 Larry (5) 1 1 1 1 0 *Directed Connections (Arcs) 13 1 2 1 3 1 4 1 5 2 1 2 3 3 4 3 5 3 2 5 1 5 4 5 3 5 2 ROWS è COLUMNS *How to Read the Edge List: (Person in Column 1 is friends with Person in Column 2)
- 23. 1 2 3 4 5 --------------------------- Daniel (1) 0 1 1 1 1 Jennifer (2) 1 0 1 0 0 Josh (3) 0 1 0 1 1 Bill (4) 0 0 0 0 0 Larry (5) 1 1 1 1 0 From a Survey to a Network
- 24. A Quick Example of a Dynamic Network
- 25. United States Supreme Court To Play Movie of the Early SCOTUS Jurisprudence: http://vimeo.com/9427420
- 27. Consumer Data Knowing Consumer Co-Purchases can help ensure that “Loss Leader” Discounts can be recouped with other purchases
- 29. Transportation Networks We might be interested in developing transportation systems that are minimize total travel time per passenger
- 30. Power Grids We might be interested in developing Power Systems that are Globally Robust to Local Failure
- 32. Some Recent Network Related Publications Special Issue: Complex systems and Networks July 24, 2009 Special 90th anniversary Issue: May 7, 2007
- 34. The Origin of Network Science is Graph Theory The Königsberg Bridge Problem the first theorem in graph theory Is It Possible to cross each bridge each and only once?
- 35. The Königsberg Bridge Problem Leonhard Euler proved that this was not possible Is It Possible to cross each bridge each and only once?
- 36. Eulerian and Hamiltonian Paths Eulerian path: traverse each edge exactly once If starting point and end point are the same: only possible if no nodes have an odd degree each path must visit and leave each shore If don’t need to return to starting point can have 0 or 2 nodes with an odd degree Hamiltonian path: visit each vertex exactly once
- 38. Moreno, Heider, et. al. and the Early Scholarship Focused Upon Determining the Manner in Which Society was Organized Developed early techniques to represent the social world Sociogram/ Sociograph Obviously did not have access to modern computing power
- 39. Stanley Milgram’s Other Experiment Milgram was interested in the structure of society Including the social distance between individuals While the term “six degrees” is often attributed to milgram it can be traced to ideas from hungarian author Frigyes Karinthy What is the average distance between two individuals in society?
- 41. Six Degrees of Separation? NE MA Target person worked in Boston as a stockbroker 296 senders from Boston and Omaha. 20% of senders reached target. Average chain length = 6.5. And So the term ... “Six degrees of Separation”
- 42. Six Degrees Six Degrees is a claim that “average path length” between two individuals in society is ~ 6 The idea of ‘Six Degrees’ Popularized through plays/movies and the kevin bacon game http://oracleofbacon.org/
- 43. Six Degrees of Kevin Bacon
- 44. Visualization Source: Duncan J. Watts, Six Degrees Six Degrees of Kevin Bacon
- 45. But What is Wrong with Milgram’s Logic? 150(150) = 22,500 150 3 = 3,375,000 150 4 = 506,250,000 150 5= 75,937,500,000
- 46. The Strength of ‘Weak’ Ties Does Milgram get it right? (Mark Granovetter) Visualization Source: Early Friendster – MIT Network www.visualcomplexity.com Strong and Weak Ties (Clustered v. Spanning) Clustering ---- My Friends’ Friends are also likely to be friends
- 47. So Was Milgram Correct? Small Worlds (i.e. Six Degrees) was a theoretical and an empirical Claim The Theoretical Account Was Incorrect The Empirical Claim was still intact Query as to how could real social networks display both small worlds and clustering? At the Same time, the Strength of Weak Ties was also an Theoretical and Empirical proposition