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

Class 11
Network Analysis + Law
Legal Analytics
Professor Daniel Martin Katz
Professor Michael J Bommarito II
legalanalyticscourse.com

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
Relationships Between Units such as
Actors, 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 Congress
Spread 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 United States 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 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

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?

Edges
Alice
Bill
Carrie
David
Ellen
Arcs

Edges
Alice Bill
Carrie
David
Ellen
Arcs

Edges Alice Bill
Carrie
David
Ellen
Arcs

Alice Bill
David
Carrie
Ellen
A Full Representation
of the Social Network

Bill
David
Carrie
Ellen
Alice
(With Node Weighting)

Bill
David
Carrie
Ellen
(With Node Weighting
and Edge Weighting)
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 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)

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 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 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/

Some Other
Examples
of Networks

Consumer Data
Knowing Consumer Co-Purchases can help ensure that “Loss
Leader” Discounts can be recouped with other purchases

Corporate Boards
http://www.theyrule.net/

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/

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
anniversary Issue:
May 7, 2007

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
(Pronounced Oil-er)
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 point
can have 0 or 2 nodes with an odd degree
Hamiltonian path: visit
each vertex exactly once

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/

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

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

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

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 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

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

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

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

1 mode
Actor to Actor
Could be Binary
(0,1)
Did they
Co-Appear?
Different Forms of

Different Forms of
1 mode
Actor to Actor
Could also be
Weighted
(I.E. Edge Weights by
Number of
Co-Appearences)

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 Components
Shortest Paths
Density

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

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

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

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

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?

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

We are often interested in whether
the graph has a single or multiple
connected components
Strong Components
Giant Component
Weak Components

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)

Netlogo
Please DownLoad Netlogo as we
will be using it occasionally
throughout this tutorial
Wilensky (1999)

Open “Giant Component” from
the netlogo models Library

Notice the
fraction of
nodes in the
giant component
Notice the Size of
the “Giant
Component”
Model has
been
advanced
25+ Ticks

Model has
been
advanced
80+ Ticks
Notice the
fraction of
nodes in the
giant component
Notice the Size of
the “Giant
Component”

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

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

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

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

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]

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)]

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

Canonical Network Models
Erdős-Renyi
Random Network
Highly Clustered
Network
Watts-Strogatz
Small World Network
Barabási-Albert
Preferential
Attachment Network

Why are Degree
Distributions Useful?
Barabási-Albert
Preferential
Attachment Network

Barabási-Albert
Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Watch the Changing
Degree Distribution

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 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)

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
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

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

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

Random
Graphs
Power Law
networks

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)

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”

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)
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

Some Additional Thoughts on the Question...

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

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
Closeness Formula:
Normalized Closeness Formula:

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

Betweenness centrality counts the
number of geodesic paths between i & k
that actor j resides on

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

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]

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

We are interested in BOTH:
to whom a webpage links
and
From whom it has received links
In Ranking a Webpage ...

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

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.

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

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

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)

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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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
Related Processes
(JLE Article)
Legal Doctrine and Legal Rules
(Sinks Paper with Application to
Patents, Legal Doctrine, etc.)

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
Network Analysis of

The Core Claim
In the Aggregate ...
Law Clerk Movements Reveal
Between Judicial Actors
Social or Professional Relationships

Network Analysis of
Judge E
Justice ZJustice Y
Judge C
Judge D
Judge B
Judge A

Network Analysis of

Highly Skewed
Distribution of Social
Authority
!

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

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 Zelner
Michael Bommarito
Eric Provins
Eitan Ingall

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 ....

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

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

Social Network Analysis of the
American Law Professoriate
Data Collection

Building A Graph Theoretic
Representation
Cornell
Harvard Penn

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
Using a Layout Algorithm

Zoomable Visualization Available @

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 PageRank™ Algorithm
Measure who is important?
Measure who is important to who is important?
Run Analysis Recursively...

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

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

Distribution of
Social Authority

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)

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 Distances Between Units
(Tversky 1977)
Non-Stationary Distances Between Entities
Both Trivial and Large Distances
Linearity Heuristic Often Works
Assuming Linearity Can Prove Misleading

Computational Model of
Information Diffusion

Why Computational
Simulation?
History only Provides a Single Model Run
Computational Simulation allows ...
Consideration of Alternative “States of the world”
Evaluation of Counterfactuals

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”

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.

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

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)

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://www.python.org/
Object Oriented Programming Language

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

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 Susceptible-Infected-Recovered

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

Example Project #3:
On the Road to the
Legal Genome Project ...
Dynamic Community Detection
&
Distance Measures for
Dynamic Citation Networks

Distance Measures for
Dynamic Citation Networks
Michael J. Bommarito II
Daniel Martin Katz
Jon Zelner
James H. Fowler

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 Citations
Bibliometric Analysis

Citations
Represent the
Fossil Record

They are the
Byproduct of
Dynamic Processes

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

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!
2010/02/11/the-development-of-structure-in-
the-citation-network-of-the-united-states-
supreme-court-now-in-hd/

Six Degrees of Marbury v. Madison

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

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

Some
Papers
For
Your
Consideration

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