Network Analysis and Law: Introductory Tutorial @ Jurix 2011 Meeting (Vienna)

Network Analysis and the Law

Daniel Martin KatzMichigan State University

College of Law

Michael J. Bommarito IICenter for Study of

Complex Systems

Jurix 2011 Tutorial @ Universität Wien

!

My Background

Assistant Professor of LawMichigan State University

Former NSF IGERT Fellow,University of Michigan

Center for the Study of Complex Systems(2009-2010)

PhDPolitical Science & Public Policy

University of Michigan(2011)

JDUniversity of Michigan

Law School(2005)

My Background

Former NSF IGERT Fellow,University of Michigan

Center for the Study of Complex Systems

PhD Pre-CandidateDept. of Political Science

University of Michigan

Masters DegreeFinancial EngineeringUniversity of Michigan

Blog:

Daniel Martin Katz(Michigan State

University - College of Law)

Michael Bommarito II

(Michigan Complex Systems)

JonZelner

(PrincetonEcology & Evolutionary

Biology)

PrimaryContact

Information

[email protected]

http://www.law.msu.edu/faculty_staff/profile.php?

prof=780

http://computationallegalstudies.com/

mailto:[email protected]

mailto:[email protected]

http://www.law.msu.edu/faculty_staff/profile.php?prof=780






http://computationallegalstudies.com


Outline of Our Session

Network Analysis: An Extended Primer

Network Analysis & Law

The Frontier of Network Analysis & Law

Legal ElitesDiffusion and other Related ProcessesLegal Doctrine and Legal Rules

Advanced Network Science Topics Community Detection ERGM / P* ModelsSocial Epidemiology

Distance Measures for Dynamic Citation NetworksDynamic Community DetectionThe Judicial Collaborative Filter (Judge Aided Info Retrevial)

Network Analysis: An Extended Primer

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

http://jhfowler.ucsd.edu

http://jhfowler.ucsd.edu

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 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?


Edges

Alice

Bill

Carrie

David

Ellen

Arcs


Edges

Alice Bill

Carrie

David

Ellen

Arcs


Edges Alice BillCarrie

David

Ellen

Arcs


Alice Bill

David

Carrie

Ellen

A Full Representation of the Social Network


Bill

David

Carrie

Ellen


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)


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 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/

http://vimeo.com/9427420

http://vimeo.com/9427420

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/

http://www.theyrule.net

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 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 (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 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/

http://oracleofbacon.org

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

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 stockbrokersend 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

http://research.yahoo.com/pub/2397

http://research.yahoo.com/pub/2397

2 mode

Actors and

Movies

Different Forms of Network Representation

1 mode

Actor to Actor

Could be Binary (0,1)

Did they Co-Appear?



1 mode

Actor to Actor

Could also beWeighted

(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

In the Watts -Strogatz Model 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?

DensityWhat fraction are present?density = e / emax

For example, out of 12possible 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

NetlogoBasic 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


giant component

Notice the Size of the “Giant

Component”


Model has been

advanced 120+ Ticks


giant component

Notice the Size of the “Giant Component”now = “num-nodes”

in the slider

Degree Distributions

outdegreehow many directed edges (arcs) originate at a node

indegreehow 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

Highly Clustered Highly Clustered

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











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)



http://www.barabasilab.com/pubs/CCNR-ALB_Publications/199910-15_Science-Emergence/199910-15_Science-Emergence.pdf




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

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

Smith (2007)U.S. Law Reviews

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

For example various centrality measures have been developed

Degree

Closeness

Here is a non-exhaustive List:

Betweenness

Hubs/Authorities

DegreeDegree 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


ask yourself, in which case does “degree” appear to capture the most important actors?


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]

http://dx.doi.org/10.1073/pnas.122653799




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

http://www.cs.cornell.edu/home/kleinber/auth.pdf




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: acceptsmicrosoft excel files

Medium: requires the .net / .paj

file setup

Hard: has lots of features

(R or Python)

Daniel Martin Katz Eric Provins!

Introduction to Computing for Complex Systems (Session XVII)!

Access A Full Step By Step

Tutorial for Pajek

The Slides From My Intro to Computing

for Complex Systems

Access Using this Tab

Network Analysis Software

Just Download Pajek and Use the Tutorial

You should download it to your personal machine

MAC Users Note: It is a PC only Program so you will need something like crossover or you will have to multiboot

http://pajek.imfm.si/doku.php?id=download

http://pajek.imfm.si/doku.php

http://pajek.imfm.si/doku.php

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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Diffusion / Social Epidemiology

We Will Discuss An Applied Case Later Later But If You Want to Learn to How To Program the SIR Model in Python





BREAK FOR 15 Minutes

We Will Next Move Into Applied Network Analysis

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, 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

Daniel Martin Katz Derek K. Stafford

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 Federal Judiciary

The Core Claim

In the Aggregate ...

Law Clerk Movements Reveal

Between Judicial Actors

Social or Professional Relationships


Judge E

Justice ZJustice Y

Judge C

Judge D

Judge BJudge A

An Sample Line of Dataset


Highly Skewed Distribution of Social

Authority

!

Thirty Most Central

Non-SCOTUSFederal Judges

(1995-2005)

(Eigenvector Centrality)

Thirty Most Central Federal Judges (1995-2004)

(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 KatzJosh Gubler Jon Zelner

Michael BommaritoEric 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

Cornell University Law School




Building A Graph Theoretic Representation

Cornell

Harvard Penn


Cornell

Harvard Penn


Cornell

Harvard Penn


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

Visualizing a Full NetworkUsing 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 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 Harvard2 1 0.9048631 Yale3 5 0.8511497 Michigan4 4 0.7952253 Columbia5 5 0.7737389 Chicago6 8 0.7026757 NYU7 1 0.6668868 Stanford8 8 0.6607399 Berkeley9 10 0.6457157 Penn

10 10 0.6255498 Georgetown11 5 0.5854464 Virginia12 14 0.5014904 Northwestern13 10 0.4138745 Duke14 10 0.4075353 Cornell15 15 0.3977734 Texas16 28 0.3787268 Wisconsin17 19 0.3273598 UCLA18 24 0.2959581 Illinois19 28 0.2919847 Boston University20 28 0.2513371 Minnesota21 24 0.2403289 Iowa22 28 0.2275534 Indiana23 19 0.2235015 George

Washington24 16 0.2174677 Vanderbilt25 41 0.2012442 Florida

Hub Score Rank

US News Peer

Assessment Hub

Score Institution

26 24 0.1999686 UC Hastings27 34 0.1974877 Tulane28 28 0.1749897 USC29 35 0.1702638 Ohio State30 24 0.1586516 Boston College31 72 0.1543831 Syracuse32 19 0.1537236 UNC33 56 0.1525355 Case Western34 82 0.1511569 Northeastern35 19 0.1428239 Notre Dame36 56 0.1286375 Temple37 82 0.1232289 Rutgers Camden38 56 0.1227421 Kansas39 64 0.1213358 Connecticut40 47 0.1198901 American41 34 0.1162101 Fordham42 64 0.1150860 Kentucky43 106 0.1148082 Howard44 47 0.1125957 Maryland45 28 0.1101975 William & Mary46 56 0.1058079 Colorado47 19 0.1041129 Emory48 17 0.1031490 Washington & Lee49 72 0.1027442 Miami50 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



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 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


38 56 0.1227421 Kansas


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


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western

34 82 0.1511569 Northeastern35 19 0.1428239 Notre Dame

36 56 0.1286375 Temple


38 56 0.1227421 Kansas


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


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western


36 56 0.1286375 Temple

37 82 0.1232289 Rutgers Camden38 56 0.1227421 Kansas


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


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western


36 56 0.1286375 Temple



40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western


36 56 0.1286375 Temple



40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


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 UVAGeorgetownPennNorthwesternTexas Duke UCLA Cornell

Wisconsin BU IllinoisMinnesota

Top 20 Institutions (By Raw Placements)

!

!

Highly Skewed Nature ofLegal 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 DistancesLinearity Heuristic Often WorksAssuming 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 SocializationSignal 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

A Sample Run of the Model




Run a Simulationon 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 TypicallyRequired for Full Scale Implementation

We Used Python


http://www.python.org/

Object Oriented Programming Language



http://www.python.org

http://www.python.org

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 SchoolsExponential, 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/LateralsCurrent Collecting Data

Database Linkage to Articles/CitationsWorking with Content Providers

Empirical Evaluation of SimulationComputational LingusiticsText 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 IIDaniel 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 Citations

Bibliometric Analysis

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



We Decided to Go Back to First

Principles

Growth Rules For Citation Networks

Dynamic Directed Acyclic Graphs


Examples: Academic Articles


Examples: Academic Articles

Judicial Citations


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://computationallegalstudies.com/2010/02/11/the-development-of-structure-in-

the-citation-network-of-the-united-states-supreme-court-now-in-hd/

http://tinyurl.com/yjt3rbv


























































































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:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1472037

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1472037



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




http://people.kzoo.edu/~perdi/

http://people.kzoo.edu/~perdi/

Some Papers

For Your

Consideration

Click Here to

Access

@computational

Thank You For Your Attention!

Education

Network Analysis and Law: Introductory Tutorial @ Jurix 2011 Meeting (Vienna)