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Class 11
Network Analysis + Law
Legal Analytics
Professor Daniel Martin Katz
Professor Michael J Bommarito II
legalanalyti...
Introduction to Network Analysis
Our session will be presented in two parts:
Network Analysis + Law
Network Analysis:
An Extended Primer
Introduction to
Network Analysis
What is a Network?
What is a Social Network?
Mathematical Representation of the
Relations...
Introduction to
Network Analysis
Interdisciplinary Enterprise
Applied Math
(Graph Theory, Matrix Algebra, etc.)
Statistica...
Social Science
For Images and Links to
Underlying projects:
http://jhfowler.ucsd.edu/
3D HiDef SCOTUS Movie
Co-Sponsorship...
Social Science
The 2004 Political Blogosphere
(Adamic & Glance)
High School Friendship
(Moody)
Roll Call Votes in United S...
Physical and
Biological
Sciences
For Images and Links to
Underlying projects:
http://www.visualcomplexity.com/vc/
Computer Science
Mapping
of the
Code
Networks are ways
to represent
dependancies
between software
Computer Science
Internet is one of
the largest
known and most
important networks
Computer Science
Mapping
the
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 Re...
Edges
Alice
Bill
Carrie
David
Ellen
Arcs
Terminology & Examples
Edges
Alice Bill
Carrie
David
Ellen
Arcs
Terminology & Examples
Edges Alice Bill
Carrie
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 &...
A Survey Based Example
“Which of the above individuals
do you consider a close friend?”
Image We Surveyed 5 Actors:
(1) Da...
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 ...
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
La...
A Quick Law Based
Example of a
Dynamic Network
United States Supreme Court
To Play Movie of the Early SCOTUS Jurisprudence:
http://vimeo.com/9427420
Documentation is Ava...
Some Other
Examples
of Networks
Consumer Data
Knowing Consumer Co-Purchases can help ensure that “Loss
Leader” Discounts can be recouped with other purcha...
Corporate Boards
http://www.theyrule.net/
Transportation Networks
We might be interested in developing
transportation systems that are minimize
total travel time pe...
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/
The United
States Code
http://computationallegalstudies.com/
+
Hierarchical
Structure
Some Recent
Network Related
Publications
Special Issue:
Complex systems
and Networks
July 24, 2009
Special 90th
anniversar...
History of
Network Science
The Origin of Network
Science is Graph Theory
The Königsberg Bridge Problem
the first theorem in graph theory
Is It Possib...
The Königsberg Bridge Problem
Leonhard Euler
(Pronounced Oil-er)
proved that this
was not possible
Is It Possible to
cross...
Eulerian and
Hamiltonian Paths
Eulerian path: traverse
each edge exactly once
If starting point and end point are the same...
Modern
Network Science
Moreno, Heider, et. al.
and the Early Scholarship
Focused Upon Determining the Manner in
Which Society was Organized
Devel...
Stanley Milgram’s
Other Experiment
Milgram was interested in the
structure of society
Including the social distance
betwee...
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...
Six Degrees
Six Degrees is a claim that “average path
length” between two individuals in society
is ~ 6
The idea of ‘Six D...
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 Net...
So Was Milgram Correct?
Small Worlds (i.e. Six Degrees) was a theoretical
and an empirical Claim
The Theoretical Account W...
Watts and Strogatz (1998)
A few random links in an otherwise clustered
graph yields the types of small world
properties fo...
Watts and Strogatz (1998)
A Small Amount of Random Rewiring or
Something akin to Weak Ties—Allows for
Clustering and Small...
Different Form of
Network Representation
1 mode
2 mode
Back to the
Milgram
Experiment
The Milgram Experiment
How did the successful subjects actually
succeed?
How did they manage to get the envelope
from nebr...
Search in Networks
Most individuals do not know the path to
an individual who is many hops away
Must rely on some sort of ...
Search in Networks
What information about the problem might
the individual attempt to leverage?
visual by duncan watts
dim...
Follow up to
the original
Experiment
available at:
http://research.yahoo.com/pub/2397
Published in
Science in 2003
2 mode
Actors
and
Movies
Different Forms of
Network Representation
1 mode
Actor to Actor
Could be Binary
(0,1)
Did they
Co-Appear?
Different Forms of
Network Representation
Different Forms of
Network Representation
1 mode
Actor to Actor
Could also be
Weighted
(I.E. Edge Weights by
Number of
Co-...
Features of Networks
Mesoscopic Community Structures
Macroscopic Graph Level Properties
Microscopic Node Level Properties
Macroscopic Graph
Level Properties
Degree Distributions (Outdegree & Indegree)
Clustering Coefficients
Connected Component...
Shortest Paths
Shortest Paths
The shortest set of links
connecting two nodes
Also, known as the geodesic path
In many grap...
Shortest Paths
Shortest Paths
A and C are connected by
2 shortest paths
A – E – B - C
A – E – D - C
Diameter: the largest ...
Shortest Paths
I n t h e W a t t s - S t r o g a t z M o d e l
Shortest Paths are reduced by
increasing levels of random r...
Clustering Coefficients
Clustering Coefficients
Measure of the tendency of nodes
in a graph to cluster
Both a graph level ...
Density
Density = Of the connections
that could exist between n nodes
directed graph: emax = n*(n-1)!
(each of the n nodes...
Density
What fraction are present?
density = e / emax
For example, out of 12
possible connections..
this graph
this graph ...
Connected Components
We are often interested in whether
the graph has a single or multiple
connected components
Strong Com...
Netlogo
Basic Simulation
Platform for Agent
Based Modeling &
Simple Network
Simulation
http://ccl.northwestern.edu/netlogo...
Netlogo
Please DownLoad Netlogo as we
will be using it occasionally
throughout this tutorial
http://ccl.northwestern.edu/n...
Connected Components
Open “Giant Component” from
the netlogo models Library
Connected Components
Notice the
fraction of
nodes in the
giant component
Notice the Size of
the “Giant
Component”
Model ha...
Connected Components
Model has
been
advanced
80+ Ticks
Notice the
fraction of
nodes in the
giant component
Notice the Size...
Connected Components
Model has
been
advanced
120+ Ticks
Notice the
fraction of
nodes in the
giant component
Notice the Siz...
Degree Distributions
outdegree
how many directed edges (arcs)
originate at a node
indegree
how many directed edges (arcs) ...
Node Degree
from
Matrix Values
Outdegree:
outdegree for node 3 = 2,
which we obtain by summing
the number of non-zero
entr...
Degree Distributions
These are Degree Count for particular nodes
but we are also interested in the distribution
of arcs (o...
Degree Distributions
Imagine we have this 8 node network:
In-degree sequence:
[2, 2, 2, 1, 1, 1, 1, 0]
Out-degree sequence...
Degree Distributions
Imagine we have this 8 node network:
In-degree distribution:
[(2,3) (1,4) (0,1)]
Out-degree distribut...
Why are Degree
Distributions Useful?
They are the signature of a dynamic process
We will discuss in greater detail tomorro...
Canonical Network Models
Erdős-Renyi
Random Network
Highly Clustered
Network
Watts-Strogatz
Small World Network
Barabási-A...
Why are Degree
Distributions Useful?
Barabási-Albert
Preferential
Attachment Network
Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Watch the Changing...
Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Readings on Power law /
Scale free Networks
Check out Lada Adamic’s Power Law Tutorial
Describes distinctions between the ...
Power Laws Seem
to be Everywhere
Power Laws Seem
to be Everywhere
How Do I Know Something
is Actually a Power Law?
Clauset, Shalizi & Newman
http://arxiv.org/abs/0706.1062
argues for the use of MLE
instead of linear regression
Demonstrat...
Back to the Random Graph
Models for a Moment
Poisson distribution
Erdos-Renyi is the default random
graph model:
randomly ...
Back to the Random Graph
Models for a Moment
let there be n people
p is the probability that any two of them are ‘friends’...
Random
Graphs
Power Law
networks
Generating Power Law
Distributed Networks
Pseudocode for the growing power law networks:
Start with small number of nodes
...
Growing Power Law
Distributed Networks
The previous pseudocode is not a unique solution
A variety of other growth dynamics...
Just To Preview The
Application to Positive
Legal Theory ....
Power Laws Appear to be a
Common Feature of Legal Systems
Katz, et al (2011)
American Legal Academy
Katz & Stafford (2010)...
Some Additional Thoughts on the Question...
Back to
Network Measures
Node Level Measures
Sociologists have long been interested in
roles / positions that various nodes occupy with
in networks...
Degree
Degree is simply a count of the number of
arcs (or edges) incident to a node
Here the nodes are sized by degree:
Degree as a measure
of centrality
Please Calculate the “degree” of each of the nodes
Degree as a measure
of centrality
ask yourself, in which case does “degree” appear
to capture the most important actors?
Degree as a measure
of centrality
what about here, does it capture the “center”?
Closeness Centrality
Closeness is based on the inverse of the
distance of each actor to every other
actor in the network
C...
Closeness Centrality
Closeness Centrality
Betweenness Centrality
Idea is related to
bridges, weak ties
This individual may
serve an important
function
Betweenness
c...
Betweenness Centrality
Betweenness centrality counts the
number of geodesic paths between i & k
that actor j resides on
Betweenness Centrality
Check these yourself:
gjk = the number of
geodesics connecting j &
k, and
gjk = the number that
act...
Betweenness Centrality
Betweenness is a very
powerful concept
We will return when we discuss
community detection in
networ...
Hubs and Authorities
The Hubs and Authorities Algorithm
(HITS) was developed by Computer
Scientist Jon Kleinberg
Similar t...
Hubs and Authorities
We are interested in BOTH:
to whom a webpage links
and
From whom it has received links
In Ranking a W...
Hubs and Authorities
Intuition --
If we are trying to rank a webpage
having a link from the New York
Times is more of than...
Hubs and Authorities
Relies upon ideas such as recursion
Measure who is important?
Measure who is important to who
is impo...
Hubs and Authorities
Hubs: Hubs are highly-valued lists for
a given query
for example, a directory page from a major encyc...
Hubs and Authorities
Hubs and Authorities has been used in a
wide number of social science articles
There exists some vari...
Calculating Centrality
Measures
Thankfully, centrality measures, etc. need not be
calculated by hand
Lots of software pack...
Advanced Network Science Topics
Community Detection
ERGM Models
Diffusion /
Social Epidemiology
http://computationallegals...
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In Both Citation and Social Networks --
Algorithm Choice Matters
!
MICHAEL!J!BOMMARITO!II!!!!!!!!!DANIEL!MARTIN!KATZ!
!
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http://computationallegalstudies.com/2009/10/11/
programming-dynamic-models-in-python/
Diffusion / Social Epidemiology
Network Analysis & Law
Mapping Social Structure of Legal Elites
(hustle & Flow Article)
Diffusion, Norm Adoption and other...
Example Project #1:
Network Analysis of the
Social Structure of the
the Federal Judiciary
Hustle & Flow: A Social Network
Analysis of the American
Federal Judiciary
the Federal Judicial Heirarchy
United States
Supreme Court
Federal Court
of Appeals
Federal District Court
What is the Social Topology of
the American Federal Judiciary?
... And How Can We Measure it?
Collected Nearly 19,000 Law Clerk ‘Events’
1995 - 2005 For All Article III Judges
Relying Upon Data From Staff Directories...
The Core Claim
In the Aggregate ...
Law Clerk Movements Reveal
Between Judicial Actors
Social or Professional Relationships
Network Analysis of
the Federal Judiciary
Judge E
Justice ZJustice Y
Judge C
Judge D
Judge B
Judge A
An Sample Line of Dataset
Network Analysis of
the Federal Judiciary
Highly Skewed
Distribution of Social
Authority
!
Thirty Most
Central
Non-SCOTUS
Federal Judges
(1995-2005)
(Eigenvector
Centrality)
(Eigenvector Centrality)
Jurist Central...
More Information Here
Daniel Katz &
Derek Stafford
(2010)
Example Project #2:
Reproduction of Hierarchy?
A Social Network Analysis of
the American Law Professoriate
Reproduction of Hierarchy?
A Social Network Analysis of the
American Law Professoriate
Daniel Martin Katz
Josh Gubler
Jon ...
Motivation for Project
Why Do Certain Paradigms, Histories, Ideas Succeed?
Function of the ‘Quality’ of the Idea
Social Fa...
Law Professors are Important Actors
Agents of Socialization
Repositories / Distributors of information
Socialize Future la...
Social Network Analysis
Method for Characterizing Diffusion / Info Flow
Method for Tracking Social Connections, etc.
Metho...
Social Network Analysis of the
American Law Professoriate
Data Collection
Cornell University
Law School
Cornell University
Law School
Cornell University
Law School
Cornell University
Law School
Building A Graph Theoretic
Representation
Cornell
Harvard Penn
Building A Graph Theoretic
Representation
Cornell
Harvard Penn
Building A Graph Theoretic
Representation
Cornell
Harvard Penn
Building A Graph Theoretic
Representation
Cornell
Harvard Penn
Building the Full Dataset
Building the Full Dataset
Building the Full Dataset
Building the Full Dataset
Building the Full Dataset
....
7,054 Law Professors
! p = {p1, p2, ... p7240}
184 ABA Accredited Institutions
n = {n1 , n2, … n184}
Full Data Set
....
Visualizing a Full Network
Visualizing a Full Network
Using a Layout Algorithm
Zoomable Visualization Available @
http://computationallegalstudies.com/
Zoomable Visualization Available @
http://computationallegalstudies.com/
A Graph-Based Measure
of Centrality
Hub Score
Score Each Institution’s Placements by
Number and Quality of Links
Normalized Score (0, 1]
Similar to the Google...
Hub
Score
Rank
US News
Peer
Assessment
Hub
Score
Institution
1 1 1.0000000 Harvard
2 1 0.9048631 Yale
3 5 0.8511497 Michig...
Hub
Score Rank
US News Peer
Assessment Score
Hub
Score
Institution
26 24 0.1999686 UC Hastings
27 34 0.1974877 Tulane
28 2...
Hub
Score Rank
US News Peer
Assessment Score
Hub
Score
Institution
26 24 0.1999686 UC Hastings
27 34 0.1974877 Tulane
28 2...
Hub
Score Rank
US News Peer
Assessment Score
Hub
Score
Institution
26 24 0.1999686 UC Hastings
27 34 0.1974877 Tulane
28 2...
Hub
Score Rank
US News Peer
Assessment Score
Hub
Score
Institution
26 24 0.1999686 UC Hastings
27 34 0.1974877 Tulane
28 2...
Hub
Score Rank
US News Peer
Assessment Score
Hub
Score
Institution
26 24 0.1999686 UC Hastings
27 34 0.1974877 Tulane
28 2...
Hub
Score Rank
US News Peer
Assessment Score
Hub
Score
Institution
26 24 0.1999686 UC Hastings
27 34 0.1974877 Tulane
28 2...
Distribution of
Social Authority
0
200
400
600
800
1,000
Harvard Yale Michigan Columbia Chicago NYU Stanford Berkeley UVA GeorgetownPennNorthwesternTexas D...




Highly Skewed Nature of
Legal Systems
Smith 2007
Post & Eisen 2000Katz & Stafford 2010
!
Implications for Rankings
Rankings only Imply Ordering ( >, =, < )
End Users tend to Conflate Ranks with
Linearized Distan...
Computational Model of
Information Diffusion
Why Computational
Simulation?
History only Provides a Single Model Run
Computational Simulation allows ...
Consideration o...
Computational Model of
Information Diffusion
We Apply a simple Disease Model to
Consider the Spread of Ideas, etc.
Clear T...
A Basic Description
of the Model
Consider a Hypothetical Idea Released
at a Given Institution
Infectiousness Probability =...
Lots of Channels of Information Diffusion
Among Legal Academics
Judicial Decisions, Law Reviews, Other Materials
Academic ...
A Sample Run of the Model
A Sample Run of the Model
A Sample Run of the Model
A Sample Run of the Model
Run a Simulation
on Your Desktop
http://computationallegalstudies.com/2009/04/22/the-revolution-will-not-be-televised-but-...
From a Single Run to
Consensus Diffusion Plot
Netlogo is Good for Model Demonstration
Regular Programming Language Typical...
From a Single Run to
Consensus Diffusion Plot
Repeated the Diffusion Simulation
Hundreds of Model Runs Per School
Yielded ...


Computational Simulation of Diffusion upon
the Structure of the American Legal Academy
Differential Host Susceptibility
Some Potential
Model Improvements?
Countervailing Information / Paradigms
S I R Model Sus...
Directions for
Future Research
Longitudinal Data
Hiring/Placement/Laterals
Current Collecting Data
Database Linkage to Art...
Example Project #3:
On the Road to the
Legal Genome Project ...
Dynamic Community Detection
&
Distance Measures for
Dynami...
Distance Measures for
Dynamic Citation Networks
Michael J. Bommarito II
Daniel Martin Katz
Jon Zelner
James H. Fowler
Imagine
Ideas
Represented as
Colors
How Can We
Track the Novel
Combination,
Mutation and
Spread of Ideas?
Information Genome Project
The Development, Mutation
and and Spread of Ideas
Precedent in Common Law Systems
Patent Citati...
Citations
Represent the
Fossil Record
They are the
Byproduct of
Dynamic Processes
Information
Genomics
Leverging the
Ideas in Network
Community
Detection
Want to Develop a
Method that can
Identify the Time
Dependant ...
Changing
Relationships
between Various
Intellectual
Concepts
(1)Patent Citations
(2) Judicial Decisions
(3) Academic Articles
Applied Traditional Methods to
SCOTUS Citation Network
Applied Traditional Methods to
SCOTUS Citation Network
#EPICFAIL
Here is Proof of the #EPICFAIL
Reported the Results
at ASNA 2009
Key Points from the
ASNA 2009 Paper
Key Points from the
ASNA 2009 Paper
Key Points from the
ASNA 2009 Paper
We Decided to Go
Back to First
Principles
Growth Rules
For Citation Networks
Dynamic Directed
Acyclic Graphs
Dynamic Directed
Acyclic Graphs
Examples:
Academic Articles
Dynamic Directed
Acyclic Graphs
Examples:
Academic Articles
Judicial Citations
Dynamic Directed
Acyclic Graphs
Examples:
Academic Articles
Judicial Citations
Patent Citations
Network Dynamics:
The Early Jurisprudence of the
United States Supreme Court
Cases Decided by
the Supreme Court
Citations in the
Current Year
Citations from
prior years
PLAY MOVIE!
http://computation...
A Formalization of D-DAG’s
Six Degrees of Marbury v. Madison
A Formalization of D-DAG’s
Basic Idea of Sink Based
Distance Measure
The Simplest Non-Trivial
Distance Measure
Flexible Framework For More
Detailed Specifications
Distance Measure
<- ->
Dendrogram
http://ssrn.com/author=627779
http://arxiv.org/abs/0909.1819available at:
Expect More in
Judicial Citation
Dynamics ....
Here is Another
Application ...
Potential Application to
Patent Citations?
Sternitzke, Bartkowski & Schramm (2008)
Potential Application to
Patent Citations?
Network Analysis of
Patent Citations
Network Analysis of
Patent Citations
http://www.eecs.umich.edu/cse/dm_11_video/erdi.mp4
http://people.kzoo.edu/~perdi/Talk By Péter Érdi
Network Analysis of
Pa...
Some
Papers
For
Your
Consideration
Legal Analytics
Class 11 - Network Analysis + Law
daniel martin katz
blog | ComputationalLegalStudies
corp | LexPredict
mi...
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito
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Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito

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Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito

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Legal Analytics Course - Class 11 - Network Analysis and Law - Professors Daniel Martin Katz + Michael J Bommarito

  1. 1. Class 11 Network Analysis + Law Legal Analytics Professor Daniel Martin Katz Professor Michael J Bommarito II legalanalyticscourse.com
  2. 2. Introduction to Network Analysis Our session will be presented in two parts: Network Analysis + Law
  3. 3. Network Analysis: An Extended Primer
  4. 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. 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. 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. 7. Social Science The 2004 Political Blogosphere (Adamic & Glance) High School Friendship (Moody) Roll Call Votes in United States Congress (Mucha, et al)
  8. 8. Physical and Biological Sciences For Images and Links to Underlying projects: http://www.visualcomplexity.com/vc/
  9. 9. Computer Science Mapping of the Code Networks are ways to represent dependancies between software
  10. 10. Computer Science Internet is one of the largest known and most important networks
  11. 11. Computer Science Mapping the Iranian Blogsphere http://cyber.law.harvard.edu/publications/2008/Mapping_Irans_Online_Public
  12. 12. Primer on Network Terminology
  13. 13. Terminology & Examples Institutions Firms States/Countries Actors NODES Other
  14. 14. Example: Nodes in an actor- based social Network Alice Bill Carrie David Ellen How Can We Represent The Relevant Social Relationships? Terminology & Examples
  15. 15. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
  16. 16. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
  17. 17. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
  18. 18. Alice Bill David Carrie Ellen A Full Representation of the Social Network Terminology & Examples
  19. 19. Bill David Carrie Ellen Terminology & Examples Alice A Full Representation of the Social Network (With Node Weighting)
  20. 20. Bill David Carrie Ellen A Full Representation of the Social Network (With Node Weighting and Edge Weighting) Terminology & Examples Alice
  21. 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. 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. 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. 24. A Quick Law Based Example of a Dynamic Network
  25. 25. United States Supreme Court To Play Movie of the Early SCOTUS Jurisprudence: http://vimeo.com/9427420 Documentation is Available Here: http://computationallegalstudies.com/2010/02/11/the-development-of-structure-in-the-citation-network-of-the- united-states-supreme-court-now-in-hd/
  26. 26. Some Other Examples of Networks
  27. 27. Consumer Data Knowing Consumer Co-Purchases can help ensure that “Loss Leader” Discounts can be recouped with other purchases
  28. 28. Corporate Boards http://www.theyrule.net/
  29. 29. Transportation Networks We might be interested in developing transportation systems that are minimize total travel time per passenger
  30. 30. Power Grids We might be interested in developing Power Systems that are Globally Robust to Local Failure
  31. 31. Campaign Contributions Networks http://computationallegalstudies.com/tag/110th-congress/
  32. 32. The United States Code http://computationallegalstudies.com/ + Hierarchical Structure
  33. 33. Some Recent Network Related Publications Special Issue: Complex systems and Networks July 24, 2009 Special 90th anniversary Issue: May 7, 2007
  34. 34. History of Network Science
  35. 35. 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?
  36. 36. The Königsberg Bridge Problem Leonhard Euler (Pronounced Oil-er) proved that this was not possible Is It Possible to cross each bridge each and only once?
  37. 37. 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. 38. Modern Network Science
  39. 39. 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
  40. 40. 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. 41. Stanley Milgram’s Other Experiment NE MA
  42. 42. 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”
  43. 43. 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/
  44. 44. Six Degrees of Kevin Bacon
  45. 45. Visualization Source: Duncan J. Watts, Six Degrees Six Degrees of Kevin Bacon
  46. 46. 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
  47. 47. 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
  48. 48. 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
  49. 49. Watts and Strogatz (1998) A few random links in an otherwise clustered graph yields the types of small world properties found by Milgram “Randomness” is key bridge between the small world result and the clustering that is commonly observed in real social networks
  50. 50. Watts and Strogatz (1998) A Small Amount of Random Rewiring or Something akin to Weak Ties—Allows for Clustering and Small Worlds Random Graphlocally Clustered
  51. 51. Different Form of Network Representation 1 mode 2 mode
  52. 52. Back to the Milgram Experiment
  53. 53. The Milgram Experiment How did the successful subjects actually succeed? How did they manage to get the envelope from nebraska to boston? this is a question regarding how individuals conduct searches in their networks Given most individuals do not know the path to distantly linked individuals
  54. 54. Search in Networks Most individuals do not know the path to an individual who is many hops away Must rely on some sort of heuristic rules to determine the possible path
  55. 55. Search in Networks What information about the problem might the individual attempt to leverage? visual by duncan watts dimensional data: send it to a stockbroker send it to closet possible city to boston
  56. 56. Follow up to the original Experiment available at: http://research.yahoo.com/pub/2397 Published in Science in 2003
  57. 57. 2 mode Actors and Movies Different Forms of Network Representation
  58. 58. 1 mode Actor to Actor Could be Binary (0,1) Did they Co-Appear? Different Forms of Network Representation
  59. 59. Different Forms of Network Representation 1 mode Actor to Actor Could also be Weighted (I.E. Edge Weights by Number of Co-Appearences)
  60. 60. Features of Networks Mesoscopic Community Structures Macroscopic Graph Level Properties Microscopic Node Level Properties
  61. 61. Macroscopic Graph Level Properties Degree Distributions (Outdegree & Indegree) Clustering Coefficients Connected Components Shortest Paths Density
  62. 62. Shortest Paths Shortest Paths The shortest set of links connecting two nodes Also, known as the geodesic path In many graphs, there are multiple shortest paths
  63. 63. Shortest Paths Shortest Paths A and C are connected by 2 shortest paths A – E – B - C A – E – D - C Diameter: the largest geodesic distance in the graph The distance between A and C is the maximum for the graph: 3
  64. 64. Shortest Paths I n t h e W a t t s - S t r o g a t z M o d e l Shortest Paths are reduced by increasing levels of random rewiring
  65. 65. Clustering Coefficients Clustering Coefficients Measure of the tendency of nodes in a graph to cluster Both a graph level average for clustering Also, a local version which is interested in cliqueness of a graph
  66. 66. Density Density = Of the connections that could exist between n nodes directed graph: emax = n*(n-1)! (each of the n nodes can connect to (n-1) other nodes) undirected graph emax = n*(n-1)/2 (since edges are undirected, count each one only once) What Fraction are Present?
  67. 67. Density What fraction are present? density = e / emax For example, out of 12 possible connections.. this graph this graph has 7, giving it a density of 7/12 = 0.58 A “fully connected graph has a density =1
  68. 68. Connected Components We are often interested in whether the graph has a single or multiple connected components Strong Components Giant Component Weak Components
  69. 69. Netlogo Basic Simulation Platform for Agent Based Modeling & Simple Network Simulation http://ccl.northwestern.edu/netlogo/ Wilensky (1999) HIV / VOTING Hawk/Dove (A Classic from Evolutionary Game Theory)
  70. 70. Netlogo Please DownLoad Netlogo as we will be using it occasionally throughout this tutorial http://ccl.northwestern.edu/netlogo/ Wilensky (1999)
  71. 71. Connected Components Open “Giant Component” from the netlogo models Library
  72. 72. Connected Components Notice the fraction of nodes in the giant component Notice the Size of the “Giant Component” Model has been advanced 25+ Ticks
  73. 73. Connected Components Model has been advanced 80+ Ticks Notice the fraction of nodes in the giant component Notice the Size of the “Giant Component”
  74. 74. Connected Components Model has been advanced 120+ Ticks Notice the fraction of nodes in the giant component Notice the Size of the “Giant Component” now = “num-nodes” in the slider
  75. 75. Degree Distributions outdegree how many directed edges (arcs) originate at a node indegree how many directed edges (arcs) are incident on a node degree (in or out) number of edges incident on a node Indegree=3 Outdegree=2 Degree=5
  76. 76. Node Degree from Matrix Values Outdegree: outdegree for node 3 = 2, which we obtain by summing the number of non-zero entries in the 3rd row Indegree: indegree for node 3 = 1, which we obtain by summing the number of non-zero entries in the 3rd column
  77. 77. Degree Distributions These are Degree Count for particular nodes but we are also interested in the distribution of arcs (or edges) across all nodes These Distributions are called “degree distributions” Degree distribution: A frequency count of the occurrence of each degree
  78. 78. Degree Distributions Imagine we have this 8 node network: In-degree sequence: [2, 2, 2, 1, 1, 1, 1, 0] Out-degree sequence: [2, 2, 2, 2, 1, 1, 1, 0] (undirected) degree sequence: [3, 3, 3, 2, 2, 1, 1, 1]
  79. 79. Degree Distributions Imagine we have this 8 node network: In-degree distribution: [(2,3) (1,4) (0,1)] Out-degree distribution: [(2,4) (1,3) (0,1)] (undirected) distribution: [(3,3) (2,2) (1,3)]
  80. 80. Why are Degree Distributions Useful? They are the signature of a dynamic process We will discuss in greater detail tomorrow Consider several canonical network models
  81. 81. Canonical Network Models Erdős-Renyi Random Network Highly Clustered Network Watts-Strogatz Small World Network Barabási-Albert Preferential Attachment Network
  82. 82. Why are Degree Distributions Useful? Barabási-Albert Preferential Attachment Network
  83. 83. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment Watch the Changing Degree Distribution
  84. 84. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  85. 85. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  86. 86. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  87. 87. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  88. 88. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  89. 89. Readings on Power law / Scale free Networks Check out Lada Adamic’s Power Law Tutorial Describes distinctions between the Zipf, Power-law and Pareto distribution http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html This is the original paper that gave rise to all of the other power law networks papers: A.-L. Barabási & R. Albert, Emergence of scaling in random networks, Science 286, 509–512 (1999)
  90. 90. Power Laws Seem to be Everywhere
  91. 91. Power Laws Seem to be Everywhere
  92. 92. How Do I Know Something is Actually a Power Law?
  93. 93. Clauset, Shalizi & Newman http://arxiv.org/abs/0706.1062 argues for the use of MLE instead of linear regression Demonstrates that a number of prior papers mistakenly called their distribution a power law Here is why you should use Maximum Likelihood Estimation (MLE) instead of linear regression You recover the power law when its present Notice spread between the Yellow and red lines
  94. 94. Back to the Random Graph Models for a Moment Poisson distribution Erdos-Renyi is the default random graph model: randomly draw E edges between N nodes There are no hubs in the network Rather, there exists a narrow distribution of connectivities
  95. 95. Back to the Random Graph Models for a Moment let there be n people p is the probability that any two of them are ‘friends’ Binomial Poisson Normal limit p small Limit large n
  96. 96. Random Graphs Power Law networks
  97. 97. Generating Power Law Distributed Networks Pseudocode for the growing power law networks: Start with small number of nodes add new vertices one by one each new edge connects to an existing vertex in proportion to the number of edges that vertex already displays (i.e. preferentially attach)
  98. 98. Growing Power Law Distributed Networks The previous pseudocode is not a unique solution A variety of other growth dynamics are possible In the simple case this is a system that extremely “sensitive to initial conditions” upstarts who garner early advantage are able to extend their relative advantage in later periods for example, imagine you receive a higher interest rate the more money you have “rich get richer”
  99. 99. Just To Preview The Application to Positive Legal Theory ....
  100. 100. Power Laws Appear to be a Common Feature of Legal Systems Katz, et al (2011) American Legal Academy Katz & Stafford (2010) American Federal Judges Geist (2009) Austrian Supreme Court Smith (2007) U.S. Supreme Court Smith (2007) U.S. Law Reviews Post & Eisen (2000) NY Ct of Appeals
  101. 101. Some Additional Thoughts on the Question...
  102. 102. Back to Network Measures
  103. 103. Node Level Measures Sociologists have long been interested in roles / positions that various nodes occupy with in networks For example various centrality measures have been developed Degree Closeness Here is a non-exhaustive List: Betweenness Hubs/Authorities
  104. 104. Degree Degree is simply a count of the number of arcs (or edges) incident to a node Here the nodes are sized by degree:
  105. 105. Degree as a measure of centrality Please Calculate the “degree” of each of the nodes
  106. 106. Degree as a measure of centrality ask yourself, in which case does “degree” appear to capture the most important actors?
  107. 107. Degree as a measure of centrality what about here, does it capture the “center”?
  108. 108. Closeness Centrality Closeness is based on the inverse of the distance of each actor to every other actor in the network Closeness Formula: Normalized Closeness Formula:
  109. 109. Closeness Centrality
  110. 110. Closeness Centrality
  111. 111. Betweenness Centrality Idea is related to bridges, weak ties This individual may serve an important function Betweenness centrality counts the number of geodesic paths between i & k that actor j resides on
  112. 112. Betweenness Centrality Betweenness centrality counts the number of geodesic paths between i & k that actor j resides on
  113. 113. Betweenness Centrality Check these yourself: gjk = the number of geodesics connecting j & k, and gjk = the number that actor i is on Note: there is also a normalized version of the formula
  114. 114. Betweenness Centrality Betweenness is a very powerful concept We will return when we discuss community detection in networks ... If you want to preview check out this paper: Michelle Girvan & Mark Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002) High Betweenness actors need not be actors that score high on other centrality measures (such as degree, etc.) [see picture to the right]
  115. 115. Hubs and Authorities The Hubs and Authorities Algorithm (HITS) was developed by Computer Scientist Jon Kleinberg Similar to the Google “PageRank” Algorithm developed by Larry Page Kleinberg is a MacArthur Fellow and has offered a number of major contributions
  116. 116. Hubs and Authorities We are interested in BOTH: to whom a webpage links and From whom it has received links In Ranking a Webpage ...
  117. 117. Hubs and Authorities Intuition -- If we are trying to rank a webpage having a link from the New York Times is more of than one from a random person’s blog HITS offers a significant improvement over measuring degree as degree treats all connections as equally valuable
  118. 118. Hubs and Authorities Relies upon ideas such as recursion Measure who is important? Measure who is important to who is important? Measure who is important to who is important to who is important ? Etc.
  119. 119. Hubs and Authorities Hubs: Hubs are highly-valued lists for a given query for example, a directory page from a major encyclopedia or paper that links to many different highly-linked pages would typically have a higher hub score than a page that links to relatively few other sources. Authority: Authorities are highly endorsed answers to a query A page that is particularly popular and linked by many different directories will typically have a higher authority score than a page that is unpopular. Note: A Given WebPage could be both a hub and an authority
  120. 120. Hubs and Authorities Hubs and Authorities has been used in a wide number of social science articles There exists some variants of the Original HITS Algorithm Here is the Original Article : Jon Kleinberg, Authoritative sources in a hyperlinked environment, Journal of the Association of Computing Machinery, 46 (5): 604–632 (1999). Note: there is a 1998 edition as well
  121. 121. Calculating Centrality Measures Thankfully, centrality measures, etc. need not be calculated by hand Lots of software packages ... in increasing levels of difficulty ... left to right Difference in functions, etc. across the packages easy: accepts microsoft excel files Medium: requires the .net / .paj file setup Hard: has lots of features (R or Python)
  122. 122. Advanced Network Science Topics Community Detection ERGM Models Diffusion / Social Epidemiology http://computationallegalstudies.com/2009/10/11/ programming-dynamic-models-in-python/
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  183. 183. Example Project #1: Network Analysis of the Social Structure of the the Federal Judiciary
  184. 184. Hustle & Flow: A Social Network Analysis of the American Federal Judiciary
  185. 185. the Federal Judicial Heirarchy United States Supreme Court Federal Court of Appeals Federal District Court
  186. 186. What is the Social Topology of the American Federal Judiciary?
  187. 187. ... And How Can We Measure it?
  188. 188. Collected Nearly 19,000 Law Clerk ‘Events’ 1995 - 2005 For All Article III Judges Relying Upon Data From Staff Directories Network Analysis of the Federal Judiciary
  189. 189. The Core Claim In the Aggregate ... Law Clerk Movements Reveal Between Judicial Actors Social or Professional Relationships
  190. 190. Network Analysis of the Federal Judiciary Judge E Justice ZJustice Y Judge C Judge D Judge B Judge A
  191. 191. An Sample Line of Dataset
  192. 192. Network Analysis of the Federal Judiciary
  193. 193. Highly Skewed Distribution of Social Authority !
  194. 194. Thirty Most Central Non-SCOTUS Federal Judges (1995-2005) (Eigenvector Centrality) (Eigenvector Centrality) Jurist Centrality Alito_Samuel_A 0.023137111 Boudin_Michael 0.094981577 Brunetti_Melvin_T 0.031860909 Cabranes_Jose_A 0.040859744 Calabresi_Guido 0.132071003 Easterbrook_Frank_H 0.029115868 Edwards_Harry_T 0.101003638 Flaum_Joel_M 0.023137202 Fletcher_William_A 0.034383907 Garland_Merrick 0.045101794 Ginsburg_Douglas_H 0.106655149 Higginbotham_Patrick_E 0.038283304 Jones_Edith_H 0.051847613 Kozinski_Alex 0.199448153 Leval_Pierre_N 0.061667539 Luttig_J_Michael 0.460086375 Niemeyer_Paul_V 0.057598972 O_Scannlain_Diarmuid 0.12676303 Posner_Richard 0.119017709 Randolph_Raymond 0.04502409 Reinhardt_Stephen_R 0.039234543 Rymer_Pamela_Ann 0.035610044 Sentelle_David_B 0.102452911 Silberman_Laurence_H 0.224592733 Tatel_David_S 0.1153377 Wald_Patricia_M 0.033537262 Wallace_Clifford 0.034474947 Wilkinson_J_Harvie 0.211140835 Williams_Stephen_F 0.090441285 Winter_Ralph_K 0.049458759
  195. 195. More Information Here Daniel Katz & Derek Stafford (2010)
  196. 196. Example Project #2: Reproduction of Hierarchy? A Social Network Analysis of the American Law Professoriate
  197. 197. Reproduction of Hierarchy? A Social Network Analysis of the American Law Professoriate Daniel Martin Katz Josh Gubler Jon Zelner Michael Bommarito Eric Provins Eitan Ingall
  198. 198. Motivation for Project Why Do Certain Paradigms, Histories, Ideas Succeed? Function of the ‘Quality’ of the Idea Social Factors also Influence the Spread of Ideas Most Ideas Do Not Persist ....
  199. 199. Law Professors are Important Actors Agents of Socialization Repositories / Distributors of information Socialize Future lawyers, Judges & law Professors Responsible for Developing Particular Legal Ideas (Brandwein (2007) ; Graber (1991), etc.) Law Professor Behavior is a Important Component of Positive Legal Theory Positive Legal Theory
  200. 200. Social Network Analysis Method for Characterizing Diffusion / Info Flow Method for Tracking Social Connections, etc. Method for Ranking Components based upon Various Graph Based Measures
  201. 201. Social Network Analysis of the American Law Professoriate Data Collection
  202. 202. Cornell University Law School
  203. 203. Cornell University Law School
  204. 204. Cornell University Law School
  205. 205. Cornell University Law School
  206. 206. Building A Graph Theoretic Representation Cornell Harvard Penn
  207. 207. Building A Graph Theoretic Representation Cornell Harvard Penn
  208. 208. Building A Graph Theoretic Representation Cornell Harvard Penn
  209. 209. Building A Graph Theoretic Representation Cornell Harvard Penn
  210. 210. Building the Full Dataset
  211. 211. Building the Full Dataset
  212. 212. Building the Full Dataset
  213. 213. Building the Full Dataset
  214. 214. Building the Full Dataset ....
  215. 215. 7,054 Law Professors ! p = {p1, p2, ... p7240} 184 ABA Accredited Institutions n = {n1 , n2, … n184} Full Data Set ....
  216. 216. Visualizing a Full Network
  217. 217. Visualizing a Full Network Using a Layout Algorithm
  218. 218. Zoomable Visualization Available @ http://computationallegalstudies.com/
  219. 219. Zoomable Visualization Available @ http://computationallegalstudies.com/
  220. 220. A Graph-Based Measure of Centrality
  221. 221. Hub Score Score Each Institution’s Placements by Number and Quality of Links Normalized Score (0, 1] Similar to the Google PageRank™ Algorithm Measure who is important? Measure who is important to who is important? Run Analysis Recursively...
  222. 222. Hub Score Rank US News Peer Assessment Hub Score Institution 1 1 1.0000000 Harvard 2 1 0.9048631 Yale 3 5 0.8511497 Michigan 4 4 0.7952253 Columbia 5 5 0.7737389 Chicago 6 8 0.7026757 NYU 7 1 0.6668868 Stanford 8 8 0.6607399 Berkeley 9 10 0.6457157 Penn 10 10 0.6255498 Georgetown 11 5 0.5854464 Virginia 12 14 0.5014904 Northwestern 13 10 0.4138745 Duke 14 10 0.4075353 Cornell 15 15 0.3977734 Texas 16 28 0.3787268 Wisconsin 17 19 0.3273598 UCLA 18 24 0.2959581 Illinois 19 28 0.2919847 Boston University 20 28 0.2513371 Minnesota 21 24 0.2403289 Iowa 22 28 0.2275534 Indiana 23 19 0.2235015 George Washington24 16 0.2174677 Vanderbilt 25 41 0.2012442 Florida Hub Score Rank US News Peer Assessment Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo Hub Scores
  223. 223. Hub Score Rank US News Peer Assessment Score Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  224. 224. Hub Score Rank US News Peer Assessment Score Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  225. 225. Hub Score Rank US News Peer Assessment Score Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  226. 226. Hub Score Rank US News Peer Assessment Score Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  227. 227. Hub Score Rank US News Peer Assessment Score Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  228. 228. Hub Score Rank US News Peer Assessment Score Hub Score Institution 26 24 0.1999686 UC Hastings 27 34 0.1974877 Tulane 28 28 0.1749897 USC 29 35 0.1702638 Ohio State 30 24 0.1586516 Boston College 31 72 0.1543831 Syracuse 32 19 0.1537236 UNC 33 56 0.1525355 Case Western 34 82 0.1511569 Northeastern 35 19 0.1428239 Notre Dame 36 56 0.1286375 Temple 37 82 0.1232289 Rutgers Camden 38 56 0.1227421 Kansas 39 64 0.1213358 Connecticut 40 47 0.1198901 American 41 34 0.1162101 Fordham 42 64 0.1150860 Kentucky 43 106 0.1148082 Howard 44 47 0.1125957 Maryland 45 28 0.1101975 William & Mary 46 56 0.1058079 Colorado 47 19 0.1041129 Emory 48 17 0.1031490 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  229. 229. Distribution of Social Authority
  230. 230. 0 200 400 600 800 1,000 Harvard Yale Michigan Columbia Chicago NYU Stanford Berkeley UVA GeorgetownPennNorthwesternTexas Duke UCLA CornellWisconsin BU IllinoisMinnesota Top 20 Institutions (By Raw Placements)
  231. 231. 
 

  232. 232. Highly Skewed Nature of Legal Systems Smith 2007 Post & Eisen 2000Katz & Stafford 2010 !
  233. 233. Implications for Rankings Rankings only Imply Ordering ( >, =, < ) End Users tend to Conflate Ranks with Linearized Distances Between Units (Tversky 1977) Non-Stationary Distances Between Entities Both Trivial and Large Distances Linearity Heuristic Often Works Assuming Linearity Can Prove Misleading
  234. 234. Computational Model of Information Diffusion
  235. 235. Why Computational Simulation? History only Provides a Single Model Run Computational Simulation allows ... Consideration of Alternative “States of the world” Evaluation of Counterfactuals
  236. 236. Computational Model of Information Diffusion We Apply a simple Disease Model to Consider the Spread of Ideas, etc. Clear Tradeoff Between Structural Position in the Network and “Idea Infectiousness”
  237. 237. A Basic Description of the Model Consider a Hypothetical Idea Released at a Given Institution Infectiousness Probability = p Two Forms Diffusion... Direct Socialization Signal Giving to Former Students Infect neighbors, neighbors-neighbors, etc.
  238. 238. Lots of Channels of Information Diffusion Among Legal Academics Judicial Decisions, Law Reviews, Other Materials Academic Conferences, Other Professional Orgs SSRN, Legal Blogosphere, etc. Channels of Diffusion Other Channels of Information Dissemination Legal Socialization / Training
  239. 239. A Sample Run of the Model
  240. 240. A Sample Run of the Model
  241. 241. A Sample Run of the Model
  242. 242. A Sample Run of the Model
  243. 243. Run a Simulation on Your Desktop http://computationallegalstudies.com/2009/04/22/the-revolution-will-not-be-televised-but-will-it- come-from-harvard-or-yale-a-network-analysis-of-the-american-law-professoriate-part-iii/ (Requires Java 5.0 or Higher)
  244. 244. From a Single Run to Consensus Diffusion Plot Netlogo is Good for Model Demonstration Regular Programming Language Typically Required for Full Scale Implementation We Used Python http://ccl.northwestern.edu/netlogo/ http://www.python.org/ Object Oriented Programming Language
  245. 245. From a Single Run to Consensus Diffusion Plot Repeated the Diffusion Simulation Hundreds of Model Runs Per School Yielded a Consensus Plot for Each School Results for Five Emblematic Schools Exponential, linear and sub-linear
  246. 246. 
 Computational Simulation of Diffusion upon the Structure of the American Legal Academy
  247. 247. Differential Host Susceptibility Some Potential Model Improvements? Countervailing Information / Paradigms S I R Model Susceptible-Infected-Recovered
  248. 248. Directions for Future Research Longitudinal Data Hiring/Placement/Laterals Current Collecting Data Database Linkage to Articles/Citations Working with Content Providers Empirical Evaluation of Simulation Computational Lingusitics Text Mining, Sentiment Coding
  249. 249. Example Project #3: On the Road to the Legal Genome Project ... Dynamic Community Detection & Distance Measures for Dynamic Citation Networks
  250. 250. Distance Measures for Dynamic Citation Networks Michael J. Bommarito II Daniel Martin Katz Jon Zelner James H. Fowler
  251. 251. Imagine
  252. 252. Ideas
  253. 253. Represented as Colors
  254. 254. How Can We Track the Novel Combination, Mutation and Spread of Ideas?
  255. 255. Information Genome Project The Development, Mutation and and Spread of Ideas Precedent in Common Law Systems Patent Citations Bibliometric Analysis
  256. 256. Citations Represent the Fossil Record
  257. 257. They are the Byproduct of Dynamic Processes
  258. 258. Information Genomics
  259. 259. Leverging the Ideas in Network Community Detection
  260. 260. Want to Develop a Method that can Identify the Time Dependant ...
  261. 261. Changing Relationships between Various Intellectual Concepts
  262. 262. (1)Patent Citations (2) Judicial Decisions (3) Academic Articles
  263. 263. Applied Traditional Methods to SCOTUS Citation Network
  264. 264. Applied Traditional Methods to SCOTUS Citation Network #EPICFAIL
  265. 265. Here is Proof of the #EPICFAIL
  266. 266. Reported the Results at ASNA 2009
  267. 267. Key Points from the ASNA 2009 Paper
  268. 268. Key Points from the ASNA 2009 Paper
  269. 269. Key Points from the ASNA 2009 Paper
  270. 270. We Decided to Go Back to First Principles
  271. 271. Growth Rules For Citation Networks
  272. 272. Dynamic Directed Acyclic Graphs
  273. 273. Dynamic Directed Acyclic Graphs Examples: Academic Articles
  274. 274. Dynamic Directed Acyclic Graphs Examples: Academic Articles Judicial Citations
  275. 275. Dynamic Directed Acyclic Graphs Examples: Academic Articles Judicial Citations Patent Citations
  276. 276. Network Dynamics: The Early Jurisprudence of the United States Supreme Court
  277. 277. Cases Decided by the Supreme Court Citations in the Current Year Citations from prior years PLAY MOVIE! http://computationallegalstudies.com/ 2010/02/11/the-development-of-structure-in- the-citation-network-of-the-united-states- supreme-court-now-in-hd/
  278. 278. A Formalization of D-DAG’s
  279. 279. Six Degrees of Marbury v. Madison
  280. 280. A Formalization of D-DAG’s
  281. 281. Basic Idea of Sink Based Distance Measure
  282. 282. The Simplest Non-Trivial Distance Measure
  283. 283. Flexible Framework For More Detailed Specifications
  284. 284. Distance Measure <- -> Dendrogram
  285. 285. http://ssrn.com/author=627779 http://arxiv.org/abs/0909.1819available at:
  286. 286. Expect More in Judicial Citation Dynamics ....
  287. 287. Here is Another Application ...
  288. 288. Potential Application to Patent Citations?
  289. 289. Sternitzke, Bartkowski & Schramm (2008) Potential Application to Patent Citations?
  290. 290. Network Analysis of Patent Citations
  291. 291. Network Analysis of Patent Citations
  292. 292. http://www.eecs.umich.edu/cse/dm_11_video/erdi.mp4 http://people.kzoo.edu/~perdi/Talk By Péter Érdi Network Analysis of Patent Citations
  293. 293. Some Papers For Your Consideration
  294. 294. Legal Analytics Class 11 - Network Analysis + Law daniel martin katz blog | ComputationalLegalStudies corp | LexPredict michael j bommarito twitter | @computational blog | ComputationalLegalStudies corp | LexPredict twitter | @mjbommar more content available at legalanalyticscourse.com site | danielmartinkatz.com site | bommaritollc.com

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