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

Network Analysis and the Law Jurix 2011 Tutorial @ Universität Wien ! Daniel Martin Katz Michael J. Bommarito II Michigan State University Center for Study of College of Law Complex Systems

My Background Assistant Professor of Law Michigan State University PhD Political Science & Public Policy University of Michigan (2011) Former NSF IGERT Fellow, University of MichiganCenter for the Study of Complex Systems (2009-2010) JD University of Michigan Law School (2005)

My Background PhD Pre-Candidate Dept. of Political Science University of Michigan Masters Degree Financial Engineering University of Michigan Former NSF IGERT Fellow, University of Michigan Center for the Study of Complex Systems

Blog:Daniel Martin Katz (Michigan State University - College of Law) Michael Bommarito II(Michigan Complex Systems) Jon Zelner (Princeton Ecology & Evolutionary Biology)

Primary ContactInformation katzd@law.msu.edu http://www.law.msu.edu/ faculty_staff/profile.php? prof=780http://computationallegalstudies.com/

Outline of Our SessionNetwork Analysis: An Extended PrimerAdvanced Network Science Topics Community Detection ERGM / P* Models Social EpidemiologyNetwork Analysis & Law Legal Elites Diffusion and other Related Processes Legal Doctrine and Legal RulesThe Frontier of Network Analysis & Law Distance Measures for Dynamic Citation Networks Dynamic Community Detection The Judicial Collaborative Filter (Judge Aided Info Retrevial)

Network Analysis:An Extended Primer

Introduction to Network AnalysisWhat is a Network? Mathematical Representation of the Relationships Between Units such as Actors, Institutions, Software, etc.What is a Social Network? Special class of graph Involving Particular Units and Connections

Introduction to Network AnalysisInterdisciplinary Enterprise Applied Math (Graph Theory, Matrix Algebra, etc.) Statistical Methods Social Science Physical and Biological Sciences Computer Science

Social ScienceCo-Sponsorship in Congress Spread of Obesity 3D HiDef SCOTUS Movie Hiring and Placement of Political Science PhD’s For Images and Links to Underlying projects: http://jhfowler.ucsd.edu/

Social ScienceThe 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 ScienceNetworks are ways Mappingto represent of thedependancies Codebetween software

Computer Science Internet is one of the largest known and mostimportant networks

Computer Science Mapping the Iranian Blogspherehttp://cyber.law.harvard.edu/publications/2008/Mapping_Irans_Online_Public

Primer on NetworkTerminology

Terminology & ExamplesNODES Institutions Firms Actors Other States/Countries

Terminology & Examples AliceExample: Nodes in an actor- based social Network Bill CarrieHow Can We Represent TheRelevant Social Relationships? David Ellen

Terminology & Examples AliceArcs Bill CarrieEdges David Ellen

Terminology & ExamplesArcs Alice Bill CarrieEdges David Ellen

Terminology & ExamplesArcs Carrie Alice BillEdges David Ellen

Terminology & Examples DavidCarrie Alice Bill A Full Representation of the Social Network Ellen

Terminology & Examples DavidCarrie Alice Bill A Full Representation of the Social Network Ellen (With Node Weighting)

Terminology & Examples DavidCarrie Alice Bill A Full Representation of the Social Network Ellen (With Node Weighting and Edge Weighting)

A Survey Based ExampleImage We Surveyed 5 Actors: (1) Daniel, (2) Jennifer, (3) Josh, (4) Bill, (5) Larry“Which of the above individualsdo you consider a close friend?”

From an EdgeList to Matrix *Directed Connections (Arcs) 13 1 2 1 3 1 4 12345 1 5 --------------------------- 2 1 Daniel (1) 0 1 1 1 1 2 3 Jennifer (2) 1 0 1 0 0 3 4 Josh (3) 0 1 0 1 1 3 5 Bill (4) 0 0 0 0 0 3 2 Larry (5) 1 1 1 1 0 5 1 5 4 5 3 5 2ROWS è COLUMNS*How to Read the Edge List: (Person in Column 1 is friends with Person in Column 2)

12345 ---------------------------From a Survey Daniel (1) 0 1 1 1 1 Jennifer (2) 1 0 1 0 0to a Network Josh Bill (3) 0 1 0 1 1 (4) 0 0 0 0 0 Larry (5) 1 1 1 1 0

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 Examplesof Networks

Consumer DataKnowing 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 developingtransportation systems that are minimize total travel time per passenger

Power GridsWe might be interested indeveloping Power Systemsthat are Globally Robustto Local Failure

Campaign Contributions Networks http://computationallegalstudies.com/tag/110th-congress/

The United States CodeHierarchical Structure + http://computationallegalstudies.com/

Some Recent Network Related Publications Special 90th Special Issue: anniversary Issue:Complex systems May 7, 2007 and Networks July 24, 2009

History ofNetwork Science

The Origin of Network Science is Graph TheoryThe Königsberg Bridge Problem the first theorem in graph theoryIs It Possible to cross each bridgeeach and only once?

The Königsberg Bridge Problem Is It Possible to cross each bridge each and only once? Leonhard Euler (Pronounced Oil-er) proved that this was not possible

Eulerian and Hamiltonian PathsIf starting point and end point are the same: only possible if no nodes have an odd degree each path must visit and leave each shoreIf don’t need to return to starting pointcan have 0 or 2 nodes with an odd degree Eulerian path: traverse Hamiltonian path: visit each edge exactly once each vertex exactly once

ModernNetwork Science

Moreno, Heider, et. al.and the Early ScholarshipFocused Upon Determining the Manner inWhich Society was OrganizedDeveloped early techniques to represent thesocial world Sociogram/ SociographObviously did nothave access tomodern computingpower

Stanley Milgram’s Other Experiment Milgram was interested in the structure of society Including the social distance between individuals What is the average distance between two individuals in society?While the term “six degrees” is oftenattributed to milgram it can be traced to ideasfrom hungarian author Frigyes Karinthy

Stanley Milgram’sOther Experiment MA NE

Six Degrees of Separation?Target person worked in Boston as a stockbroker296 senders from Boston and Omaha.20% of senders reached target.Average chain length = 6.5. MA NEAnd So the term ...“Six degrees of Separation”

Six DegreesSix Degrees is a claim that “average pathlength” between two individuals in societyis ~ 6The idea of ‘Six Degrees’ Popularizedthrough plays/movies and the kevinbacon game http://oracleofbacon.org/

Six Degrees of Kevin Bacon

Six Degrees of Kevin Bacon Visualization Source: Duncan J. Watts, Six Degrees

But What is Wrong with Milgram’s Logic?150(150) = 22,500150 3 = 3,375,000150 4 = 506,250,000150 5= 75,937,500,000

The Strength of ‘Weak’ TiesDoes Milgram getit right? (Mark Granovetter)Clustering ---- My Friends’ Friends are also likely to be friendsStrong and Weak Ties (Clustered v. Spanning) Visualization Source: Early Friendster – MIT Network www.visualcomplexity.com

So Was Milgram Correct?Small Worlds (i.e. Six Degrees) was a theoreticaland an empirical Claim The Theoretical Account Was Incorrect The Empirical Claim was still intactAt the Same time, the Strength of Weak Ties wasalso an Theoretical and Empirical propositionQuery as to how could real social networksdisplay both small worlds and clustering?

Watts and Strogatz (1998)A few random links in an otherwise clusteredgraph yields the types of small worldproperties found by Milgram“Randomness” is key bridge between the smallworld result and the clustering that iscommonly observed in real social networks

Watts and Strogatz (1998) locally Clustered Random Graph A Small Amount of Random Rewiring or Something akin to Weak Ties—Allows for Clustering and Small Worlds

Different Form ofNetwork Representation 2 mode 1 mode

Back to the MilgramExperiment

The Milgram Experiment How did the successful subjects actually succeed? Given most individuals do not know the path to distantly linked individuals How did they manage to get the envelope from nebraska to boston? this is a question regarding how individuals conduct searches in their networks

Search in NetworksMost individuals do not know the path toan individual who is many hops awayMust rely on some sort of heuristic rulesto determine the possible path

Search in NetworksWhat information about the problem mightthe individual attempt to leverage?dimensional data: send it to a stockbroker send it to closet possible city to boston visual by duncan watts

Follow up tothe original Experiment Published in Science in 2003 available at:http://research.yahoo.com/pub/2397

Different Forms ofNetwork Representation2 modeActors andMovies

Different Forms ofNetwork Representation 1 modeActor to ActorCould be Binary (0,1) Did they Co-Appear?

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

Features of NetworksMacroscopic Graph Level PropertiesMicroscopic Node Level PropertiesMesoscopic Community Structures

Macroscopic Graph Level PropertiesShortest PathsClustering CoefficientsDensityConnected ComponentsDegree Distributions (Outdegree & Indegree)

Shortest PathsShortest Paths The shortest set of links connecting two nodes Also, known as the geodesic path In many graphs, there are multiple shortest paths

Shortest PathsShortest Paths A and C are connected by 2 shortest paths A–E–B-C A–E–D-CDiameter: the largest geodesic distancein the graph The distance between A and C is the maximum for the graph: 3

Shortest PathsIn the Watts-Strogatz ModelShortest Paths are reduced byincreasing levels of random rewiring

Clustering CoefficientsClustering 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

DensityDensity = Of the connectionsthat could exist between n nodesdirected 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 / emaxFor example, out of 12possible connections..this graphthis graph has 7,giving it a density of7/12 = 0.58A “fully connected graph has a density =1

Connected ComponentsWe are often interested in whetherthe graph has a single or multipleconnected componentsStrong ComponentsWeak ComponentsGiant Component

Basic Simulation Netlogo Platform for Agent Based Modeling & Simple Network Wilensky (1999) SimulationHIV / VOTING Hawk/Dove (A Classic from Evolutionary Game Theory) http://ccl.northwestern.edu/netlogo/

Netlogo Wilensky (1999)http://ccl.northwestern.edu/netlogo/ Please DownLoad Netlogo as we will be using it occasionally throughout this tutorial

Connected Components Open “Giant Component” from the netlogo models Library

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

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

Connected Components Model has been advanced 120+ Ticks Notice the Notice the Size of the fraction of “Giant Component” nodes in the now = “num-nodes”giant component in the slider

Degree Distributionsindegreehow many directed edges (arcs) areincident on a node Indegree=3outdegreehow many directed edges (arcs)originate at a node Outdegree=2degree (in or out)number of edges incident on a node Degree=5

Node Degree fromMatrix 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

Degree DistributionsThese are Degree Count for particular nodesbut we are also interested in the distributionof arcs (or edges) across all nodesThese Distributions are called “degreedistributions”Degree distribution: A frequency count ofthe occurrence of each degree

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]

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)]

Why are DegreeDistributions Useful?They are the signature of a dynamic processWe will discuss in greater detail tomorrowConsider several canonical network models

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

Why are DegreeDistributions Useful? Barabási-Albert Preferential Attachment Network

Barabási-Albert Preferential AttachmentWatch the ChangingDegree Distribution Netlogo Models Library --> Networks --> Preferential Attachment

Barabási-Albert Preferential AttachmentNetlogo Models Library --> Networks --> Preferential Attachment

Readings on Power law / Scale free NetworksThis is the original paper that gave rise toall of the other power law networks papers: A.-L. Barabási & R. Albert, Emergence of scaling in random networks, Science 286, 509–512 (1999)Check out Lada Adamic’s Power Law TutorialDescribes distinctions between the Zipf,Power-law and Pareto distribution http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html

Power Laws Seemto be Everywhere

How Do I Know Somethingis Actually a Power Law?

Clauset, Shalizi & Newmanargues for the use of MLEinstead of linear regressionDemonstrates that a numberof prior papers mistakenly http://arxiv.org/abs/0706.1062called their distribution apower lawHere is why you should useMaximum Likelihood Estimation(MLE) instead of linearregressionYou recover the power lawwhen its presentNotice spread between theYellow and red lines

Back to the Random Graph Models for a MomentErdos-Renyi is the default randomgraph model: Poisson distributionrandomly draw E edgesbetween N nodesThere are no hubs in the networkRather, there exists a narrowdistribution of connectivities

Back to the Random Graph Models for a Momentlet there be n peoplep is the probability that any two of them are ‘friends’Binomial Poisson Normal limit p small Limit large n

Random Power LawGraphs networks

Generating Power Law Distributed NetworksPseudocode 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 NetworksThe previous pseudocode is not a unique solutionA variety of other growth dynamics are possibleIn the simple case this is a system that extremely“sensitive to initial conditions”upstarts who garner early advantage are able toextend their relative advantage in later periodsfor example, imagine you receive a higher interestrate the more money you have “rich get richer”

Just To Preview TheApplication to Positive Legal Theory ....

Power Laws Appear to be a Common Feature of Legal Systems Katz, et al (2011) Katz & Stafford (2010) Geist (2009)American Legal Academy American Federal Judges Austrian Supreme Court Smith (2007) Smith (2007) Post & Eisen (2000) U.S. Supreme Court U.S. Law Reviews NY Ct of Appeals

Some Additional Thoughts on the Question...

Back toNetwork Measures

Node Level MeasuresSociologists have long been interested inroles / positions that various nodes occupy within networksFor example various centrality measureshave been developedHere is a non-exhaustive List: Degree Closeness Betweenness Hubs/Authorities

DegreeDegree is simply a count of the number ofarcs (or edges) incident to a nodeHere the nodes are sized by degree:

Degree as a measure of centralityPlease Calculate the “degree” of each of the nodes

Degree as a measure of centralityask yourself, in which case does “degree” appear to capture the most important actors?

Degree as a measure of centralitywhat about here, does it capture the “center”?

Closeness CentralityCloseness is based on the inverse of thedistance of each actor to every otheractor in the networkCloseness Formula:Normalized Closeness Formula:

Closeness Centrality

Betweenness CentralityIdea is related tobridges, weak tiesThis individual mayserve an importantfunctionBetweennesscentrality countsthe number ofgeodesic pathsbetween i & k thatactor j resides on

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 Note: there is also a normalized gjk = the number that version of the formula actor i is on

Betweenness CentralityBetweenness is a verypowerful conceptHigh Betweenness actors neednot be actors that score high onother centrality measures (suchas degree, etc.) [see picture to the right]We will return when we discusscommunity detection innetworks ... If you want topreview check out this paper: Michelle Girvan & Mark Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002)

Hubs and AuthoritiesThe Hubs and Authorities Algorithm(HITS) was developed by ComputerScientist Jon KleinbergSimilar to the Google “PageRank”Algorithm developed by Larry PageKleinberg is a MacArthur Fellow andhas offered a number of majorcontributions

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

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

Hubs and AuthoritiesRelies 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 and AuthoritiesHubs: Hubs are highly-valued lists fora 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 highlyendorsed 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 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 MeasuresThankfully, centrality measures, etc. need not becalculated by handLots of software packages ...in increasing levels of difficulty ... left to rightDifference in functions, etc. across the packages easy: accepts Medium: requires Hard: has lots of microsoft the .net / .paj features excel files file setup (R or Python)

The Slides From My Introduction to Computing for Complex Systems (Session XVII)! Intro to Computingfor Complex Systems Daniel Martin Katz Eric Provins! Access A Full Step By Step Tutorial for Pajek Access Using this Tab

Network Analysis Software Just Download Pajek and Use the Tutorial You should download it to your personal machine http://pajek.imfm.si/doku.php?id=download MAC Users Note: It is a PC only Program so you will need something like crossover or you will have to multiboot

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 Pythonhttp://computationallegalstudies.com/2009/10/11/ programming-dynamic-models-in-python/

BREAK FOR 15 Minutes We Will Next Move IntoApplied Network Analysis

Network Analysis & LawMapping Social Structure of Legal Elites (hustle & Flow Article)Diffusion, Norm Adoption and otherRelated Processes (JLE Article)Legal Doctrine and Legal Rules (Sinks Paper with Application to Patents, etc.)

Example Project #1:Network Analysis of theSocial 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 ofthe American Federal Judiciary?

... And How Can We Measure it?

Network Analysis of the Federal JudiciaryRelying Upon Data From Staff DirectoriesCollected Nearly 19,000 Law Clerk ‘Events’1995 - 2005 For All Article III Judges

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

Network Analysis ofthe Federal Judiciary Justice Y Justice Z Judge A Judge B Judge D Judge C Judge E

An Sample Line of Dataset

Network Analysis ofthe Federal Judiciary

Highly SkewedDistribution of Social Authority !

(Eigenvector Centrality) Jurist Centrality Alito_Samuel_A 0.023137111 Boudin_Michael 0.094981577 Brunetti_Melvin_T 0.031860909 Cabranes_Jose_A 0.040859744 Thirty Most Calabresi_Guido Easterbrook_Frank_H 0.132071003 0.029115868 Central Edwards_Harry_T Flaum_Joel_M Fletcher_William_A 0.101003638 0.023137202 0.034383907 Non-SCOTUS Garland_Merrick Ginsburg_Douglas_H 0.045101794 0.106655149Federal Judges Higginbotham_Patrick_E Jones_Edith_H 0.038283304 0.051847613 (1995-2005) Kozinski_Alex Leval_Pierre_N 0.199448153 0.061667539 Luttig_J_Michael 0.460086375 Niemeyer_Paul_V 0.057598972 O_Scannlain_Diarmuid 0.12676303 (Eigenvector Posner_Richard Randolph_Raymond 0.119017709 0.04502409 Centrality) Reinhardt_Stephen_R Rymer_Pamela_Ann 0.039234543 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 ofthe 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 ProjectWhy Do Certain Paradigms, Histories, Ideas Succeed? Most Ideas Do Not Persist .... Function of the ‘Quality’ of the Idea Social Factors also Influence the Spread of Ideas

Positive Legal TheoryLaw Professors are Important Actors Repositories / Distributors of information Agents of Socialization Socialize Future lawyers, Judges & law ProfessorsResponsible for Developing Particular Legal Ideas (Brandwein (2007) ; Graber (1991), etc.)Law Professor Behavior is a ImportantComponent of Positive Legal Theory

Social Network AnalysisMethod for Tracking Social Connections, etc.Method for Characterizing Diffusion / Info FlowMethod for Ranking Components basedupon Various Graph Based Measures

Social Network Analysis of the American Law Professoriate Data Collection

Cornell University Law School

Building A Graph Theoretic RepresentationHarvard Penn Cornell

Building the Full Dataset

Building the Full Dataset ....

Full Data Set7,054 Law Professors ! p = {p1, p2, ... p7240}184 ABA Accredited Institutions n = {n1 , n2, … n184} ....

Visualizing a Full Network

Visualizing a Full NetworkUsing a Layout Algorithm

Zoomable Visualization Available @http://computationallegalstudies.com/

A Graph-Based Measure of Centrality

Hub ScoreSimilar to the Google PageRank™ Algorithm Measure who is important? Measure who is important to who is important? Run Analysis Recursively...Score Each Institution’s Placements byNumber and Quality of Links Normalized Score (0, 1]

HubScore Rank 1 US News Peer Assessment 1 Hub Score 1.0000000 Institution Harvard Hub Scores 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 Hub US News Hub 8 8 0.6607399 Berkeley Score Peer Institution Score Rank Assessment 9 10 0.6457157 Penn 10 10 0.6255498 Georgetown 26 24 0.1999686 UC Hastings 11 5 0.5854464 Virginia 27 34 0.1974877 Tulane 12 14 0.5014904 Northwestern 28 28 0.1749897 USC 13 10 0.4138745 Duke 29 35 0.1702638 Ohio State 14 10 0.4075353 Cornell 30 24 0.1586516 Boston College 15 15 0.3977734 Texas 31 72 0.1543831 Syracuse 16 28 0.3787268 Wisconsin 32 19 0.1537236 UNC 17 19 0.3273598 UCLA 33 56 0.1525355 Case Western 18 24 0.2959581 Illinois 34 82 0.1511569 Northeastern 19 28 0.2919847 Boston University 35 19 0.1428239 Notre Dame 20 28 0.2513371 Minnesota 36 56 0.1286375 Temple 21 24 0.2403289 Iowa 37 82 0.1232289 Rutgers Camden 22 28 0.2275534 Indiana 38 56 0.1227421 Kansas 23 19 0.2235015 George 39 64 0.1213358 Connecticut 24 16 0.2174677 Washington Vanderbilt 40 47 0.1198901 American 25 41 0.2012442 Florida 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 US News Peer Hub InstitutionScore Rank Assessment Score Score 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 ofSocial Authority

Top 20 Institutions (By Raw Placements)1,000 800 600400200 BU IllinoisMinnesota Northwesternexas T Duke UCLA Cornell isconsin W 0 NYU Stanford Berkeley UVA GeorgetownPenn Harvard Yale Michigan Columbia Chicago

Highly Skewed Nature of Legal Systems Smith 2007!Katz & Stafford 2010 Post & Eisen 2000

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 RunComputational Simulation allows ... Consideration of Alternative “States of the world” Evaluation of Counterfactuals

Computational Model of Information DiffusionWe 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 ModelConsider a Hypothetical Idea Releasedat a Given InstitutionInfectiousness Probability = pInfect neighbors, neighbors-neighbors, etc.Two Forms Diffusion... Direct Socialization Signal Giving to Former Students

Channels of DiffusionLots of Channels of Information DiffusionAmong Legal Academics Legal Socialization / Training Judicial Decisions, Law Reviews, Other Materials Academic Conferences, Other Professional Orgs SSRN, Legal Blogosphere, etc. Other Channels of Information Dissemination

A Sample Run of the Model

Run a Simulation on Your Desktop (Requires Java 5.0 or Higher)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/

From a Single Run toConsensus Diffusion PlotNetlogo is Good for Model Demonstration http://ccl.northwestern.edu/netlogo/Regular Programming Language TypicallyRequired for Full Scale ImplementationWe Used Python http://www.python.org/ Object Oriented Programming Language

From a Single Run to Consensus Diffusion PlotRepeated the Diffusion SimulationHundreds of Model Runs Per SchoolYielded a Consensus Plot for Each SchoolResults for Five Emblematic Schools Exponential, linear and sub-linear

Computational Simulation of Diffusion uponthe Structure of the American Legal Academy !

Some Potential Model Improvements?Differential Host SusceptibilityCountervailing Information / ParadigmsS I R Model Susceptible-Infected-Recovered

Directions for Future ResearchLongitudinal Data Hiring/Placement/Laterals Current Collecting DataDatabase Linkage to Articles/Citations Working with Content ProvidersEmpirical Evaluation of Simulation Computational Lingusitics Text Mining, Sentiment Coding

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

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

Imagine

Represented as Colors

How Can WeTrack the Novel Combination, Mutation andSpread of Ideas?

Information Genome ProjectThe Development, Mutationand and Spread of Ideas Precedent in Common Law Systems Patent Citations Bibliometric Analysis

CitationsRepresent theFossil Record

They are the Byproduct ofDynamic Processes

Information Genomics

Leverging theIdeas in Network Community Detection

Want to Develop a Method that can Identify the Time Dependant ...

Changing Relationshipsbetween 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 RulesFor Citation Networks

Dynamic Directed Acyclic Graphs

Dynamic Directed Acyclic GraphsExamples:Academic Articles

Dynamic Directed Acyclic GraphsExamples:Academic ArticlesJudicial Citations

Dynamic Directed Acyclic GraphsExamples:Academic ArticlesJudicial CitationsPatent Citations

Network Dynamics:The Early Jurisprudence of the United States Supreme Court

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/Cases Decided by Citations in the Citations fromthe Supreme Court Current Year prior years

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

available at: http://arxiv.org/abs/0909.1819 http://ssrn.com/author=627779

Expect More inJudicial Citation Dynamics ....

Here is Another Application ...

Potential Application to Patent Citations?

Potential Application to Patent Citations? Sternitzke, Bartkowski & Schramm (2008)

Network Analysis of Patent Citations

Network Analysis of Patent Citations http://www.eecs.umich.edu/cse/dm_11_video/erdi.mp4Talk By Péter Érdi http://people.kzoo.edu/~perdi/

Some Papers For YourConsideration

Click Here toAccess

@computationalThank You For Your Attention!

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

by Daniel Katz on Dec 31, 2011

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