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Complex Systems Models in the Social Sciences
(Lecture 2)
Daniel Martin KatzMichigan State University
College of Law
Introduction to Network Analysis
Introduction to Network Analysis
What is a Network?
What is a Social Network?
Mathematical Representation of theRelationships Between Units such asActors, Institutions, Software, etc.
Special class of graph Involving Particular Units and Connections
Introduction to Network Analysis
Interdisciplinary Enterprise
Applied Math(Graph Theory, Matrix Algebra, etc.)
Statistical Methods
Social Science
Physical and Biological Sciences
Computer Science
Social Science
For Images and Links to Underlying projects:
http://jhfowler.ucsd.edu/
3D HiDef SCOTUS Movie
Co-Sponsorship in CongressSpread of Obesity
Hiring and Placement of Political Science PhD’s
Social Science
The 2004 Political Blogosphere (Adamic & Glance)
High School Friendship(Moody)
Roll Call Votes in Congress(Mucha, et al)
Physical and Biological Sciences
For Images and Links to Underlying projects:
http://www.visualcomplexity.com/vc/
Computer Science
Mapping
of the
Code
Networks are waysto represent dependanciesbetween software
Computer Science
Internet is one ofthe largest
known and most important networks
Computer Science
Mappingthe
Iranian Blogsphere
http://cyber.law.harvard.edu/publications/2008/Mapping_Irans_Online_Public
Primer on Network
Terminology
Terminology & Examples
Institutions
Firms
States/Countries
Actors
NODES
Other
Example: Nodes in an actor- based social Network
Alice
Bill
Carrie
David
Ellen
How Can We Represent The Relevant Social Relationships?
Terminology & Examples
Edges
Alice
Bill
Carrie
David
Ellen
Arcs
Terminology & Examples
Edges
Alice Bill
Carrie
David
Ellen
Arcs
Terminology & Examples
Edges Alice BillCarrie
David
Ellen
Arcs
Terminology & Examples
Alice Bill
David
Carrie
Ellen
A Full Representation of the Social Network
Terminology & Examples
Bill
David
Carrie
Ellen
Terminology & Examples
Alice
A Full Representation of the Social Network(With Node Weighting)
Bill
David
Carrie
Ellen
A Full Representation of the Social Network(With Node Weighting and Edge Weighting)
Terminology & Examples
Alice
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
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 21 31 41 52 12 33 43 53 25 15 45 35 2
ROWS è COLUMNS
*How to Read the Edge List: (Person in Column 1 is friends with Person in Column 2)
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
A Quick Example of a Dynamic Network
United States Supreme Court
To Play Movie of the Early SCOTUS Jurisprudence: http://vimeo.com/9427420
Some Other Examples
of Networks
Consumer Data
Knowing Consumer Co-Purchases can help ensure that “Loss Leader” Discounts can be recouped with other purchases
Transportation Networks
We might be interested in developing transportation systems that are minimize
total travel time per passenger
Power Grids
We might be interested in developing Power Systems that are Globally Robust to Local Failure
Campaign Contributions Networks
http://computationallegalstudies.com/tag/110th-congress/
Some Recent Network Related
Publications
Special Issue: Complex systems
and NetworksJuly 24, 2009
Special 90th anniversary Issue:
May 7, 2007
History ofNetwork Science
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?
The Königsberg Bridge Problem
Leonhard Euler proved that this was not possible
Is It Possible to cross each bridge each and only once?
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 pointcan have 0 or 2 nodes with an odd degree
Hamiltonian path: visiteach vertex exactly once
ModernNetwork Science
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
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?
Stanley Milgram’s Other Experiment
NE
MA
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”
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/
Six Degrees of Kevin Bacon
Visualization Source: Duncan J. Watts, Six Degrees
Six Degrees of Kevin Bacon
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
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
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
We Will Continue Here Next Time
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