Analysis of Multistate Attorney General Litigation
Introduction
Originating in graph theory, network analysis has become a versatile tool and found extensive applications in diverse fields, such as applications to biology, economics, ecology, information science, political science, technology, and sociology. 1 Its interdisciplinary nature contributed to the advancement in understanding complex systems and relationships within various domains. Despite its well-established influence, the integration of network analysis in the study of law, law firms, and the legal industry is only recently garnering attention. 2 Network analysis in legal studies emerges as a research area with burgeoning potential to reveal legal dynamics, law firm organization, and the legal ecosystem functioning, opening new avenues for theoretical exploration and empirical research.
Legal scholarship and network analysis have become a multi-faceted discipline, serving as a tool to study the law itself, the development of legal procedures, and dynamics within the legal profession. Legal citation networks analyze the legal documents, and networks allow for create structure among case law citations. 3 Social networks have also shown how law firms incorporate innovative legal text, by combining social networks, text analysis, and survival analysis, as in Bishop, Jennejohn, and Jones (2022). Networks have been used in several domains of the law: contracts,4, institional investors5, insider trading6, shareholders7, torts8, and patents9. Early research10 examined the legal profession itself, describing interactions among attorneys and continues into current issues, such as diversity. 11
Legal social networks naturally arise in litigation cases, embodying a fluid interplay among various actors. These actors encompass the plaintiffs and defendants, representing the fundamental parties implicated in legal disputes. The complex network architecture vividly illustrates the negotiations, disputes, and interactions that transpire among these entities over the course of legal proceedings. Alternatively, the legal social network can be viewed through the lens of the attorneys and judges participating actively in these cases. This legal structure reveals the professional relationships, collaborative efforts, and legal strategies that influence the trajectory and resolution of the litigation process.
A significant contribution of this paper involves the application of social network analysis to the realm of multistate attorney general litigation. This approach offers a novel and comprehensive perspective on the complex dynamics and interconnected relationships within these legal frameworks. This study pioneers the visualization and detailed examination of the intricate networks of multistate attorney general litigation. The research uncovers previously unexplored structural complexities and patterns inherent within these legal networks.
Data
The data for the multistate attorney general litigations is from the Biden Administration. There are 64 cases with the first case filed on January 21, 2021, and the last case in our data set filed on July 17, 2023. Not all of the cases have reached a decision yet. There are 58 unique litigation targets spanning a range of policy areas, with the most cases in public health, immigration, and the environment.
These cases comprise 50 plaintiff states and occur in 23 courts. There are 465 unique attorneys and judges.
There were 44 of 64 cases or 69% of cases which sought a preliminary injunction. Of these, 13% secured a partial injunction and 25% obtatined a nationwide injunction.
Methods
Social network analysis aims to describe the interrelationships among individuals, conceptualized as the nodes within a network.12 The relationships can be represented as edges or links, highlighting varying degrees of node association. Since nodes vary in their connections, a discernible network structure emerges as nodes are added to the network. Network structures may range in patterns, from containing strong connections between a core node group surrounded by fewer periphery nodes, to connected subnetworks, or intermediary arrangements between these two extremes.
Due to the diverse array of connections in nature and quality between the nodes, the network structure may feature some central nodes – nodes with many connections in the core of the network. A fundamental aspect of network analysis is to discover the centrality to determine which nodes are the key players in the network and critical for facilitating information flow throughout the network.
In the following examples, we demonstrate the process of transforming docket data into social networks. While these examples are presented from the perspectives of states involved the litigation, the method is analagous for the attorneys and judges engaged in the legal proceedings.
All the states (attorneys and judges) are represented as network nodes. We inferred links between the nodes or edges when states collaborate on the same matter. For example, we illustrate a simple case involving a lead state and two joining states, as shown in Figure 1. Since all three states (State1, State2, and State3) participated in the case, we inferred edges between each of the nodes. The network edges demonstrate the transfer of information transfers among participants involved in a case.
The network expands in tandem with the number of cases and the involvement of states. Building upon the previous example, let us consider adding a second case where State 2 and State 4 collaborate. By aggregating the networks of the two cases, the resulting network, as portrayed in Figure 2, showcases the collective interplay of states involved across multiple legal cases.
We also show the impact on network structure when states of differing political parties are integrated into the network. Contnuing with the previous example, let us consider where the intial four states belonged to the same political party affiliation and worked together on related cases. During a presidential administration, states of contrasting political parties may engage on very disparate, unrelated cases. We introduce three additional states (5,6 and 7) to the network, each with the opposite political party to the initial set. None of the added states collaborate with any of the previous states, so a separate cluster emerges in the network, as displayed in Figure 3.
In this project, we depicted a multilayer network, which integrates various types of relationships between a set of nodes. Each layer within this multidimensional network represents a distinct dimension, corresponding to a different presidential administration. By plotting the relationships between states during each administration, the multilayer network effectively captures the transformative journey of state relationships over time, offering insights into the impact of shifts in political leadership.
Figure 4 shows a simple example of three states in each Presidential Administrative period. States may be present in multiple administrative periods.
These simple illustrations primarily focused on state nodes for expository purposes. Yet, we also incorporated attorneys and judges into their own network. This paper constructed two distinct networks, each shedding light on different aspects of multistate attorney general actions.
Plaintiff States Network: Our research involves constructing a social network that links plaintiff states engaged in attorney general litigation. Interconnections between states develop when they collaborate on the same legal cases, forming edges within the network. As multiple cases involve various states, the network evolves to reflect the dynamic nature of their legal interactions.
Litigation Network: We developed a social network encompassing all judges and attorneys, where each network node represents a litigator. Links between the individuals emerge when they participate in the same legal matter. Since these attorneys and judges frequently interact in multiple cases, the network expands to the intricacies of their ongoing collaborative relationships. We weighted the network by the number of times that two individuals interacted with each other.
After describing the construction how our networks are created, we introduce the network measures used to determine centrality within the networks.
The simplest method of measuring the centrality of a node is degree centrality. Degree centrality counts the connections a node has with other nodes. For example, in Figure 2, states 1 and 3 each have a degree centrality of 2 because they each have two edges to other nodes. State 2 has a degree centrality of 3, and state 4 has a degree centrality of 1. The node with the greatest degree centrality is state 2, because it has the most connections to other nodes.
Eigenvector centrality measures not only connections to other nodes, but how well those connections are connected. It measures the influence of a node. Highly central nodes are connected to other highly connected nodes. Values of eigenvector centrality range from 0 to 1. State 2 has the highest value of eigenvector centrality.
Betweenness centrality measures the number of shortest paths that pass through a node. It involves the calculation of all shortest paths in the network and finding which passes through each vertex. In this network, State 2 has a betweenness centrality of 2, and all the other states have a betweenness centrality of 0.
Related to betweenness centrality, closeness centrality is the reciprocal of the sum of the lengths of shortest paths (distances) between a node and all other nodes. Continuing the example for closeness: state 1 is 0.25, state 2 is 0.33, state 3 is 0.25, and state 4 is 0.2.
We could either choose one centrality metric or combine all possible centrality metrics into one score.
We also measured assortativity, the degree of mixing. Assortativity in network analysis measures the preference for nodes of a network to attach to other similar nodes. We calculated assortativity in three different categories: attorney or judge, political party affiliation, and degree centrality.
Results
The network graph displayed in Figure 5 illustrates the plaintiff states, labeled by the political party affiliation of their attorney general at the time the state joined the case. The network exhibits two prominent clusters, each dominated by respective political parties. Hence, this network displays complete assortativity. Republican states predominately associate with other Republican states, and Democrat states primariliy collaborate with fellow Democrats, without any inter-party collaboration. However, the degree assortativity, or the preference of nodes to attach to nodes of similar degree, is 0.61, revealing assortativity between states with similar number of connections.
During the Biden Administration, there were three states who had a change in the political party of their elected attorney general: Arizona, Iowa, and Virginia.
The network graph of plaintiff states is presented interactively in four plots: Figure 6, Figure 8, Figure 7, and Figure 9. Users can zoom in and out, click and drag specific nodes, pan, or rotate the network. These dynamic graphs provide an enhanced visualization experience and an appealing interface for analysis.
The geographic representation of the plaintiff state network is depicted in Figure 10, describing the spatial mapping of the states. The lines on the map represent edges connected to central points of each state. Then, we partitioned this graph by the political party of the attorney general, as demonstrated in Figure 11.
Figure 12 maps the network statistics onto the U.S. state map. Figure 12 (a) represents the degree centrality or the number of connections that each state has to other states. It shows nodes likely to hold information or quickly connect with the wider network. Interestingly, we observe larger values of centrality in the Midwest, South, and Rocky Mountain regions, particularly in Arkansas, Montana, South Carolina, Missouri, and Louisiana. Eigenvector centrality shows a more pronounced picture than the degree centrality, as shown in Figure 12 (b). Eigenvector centrality measures the influence of a node in a network, or the connections of a node’s connections. It measures influence over the entire network for a node, not just those directly connected to it. Highly connected values are near one, while less connected nodes have values near zero. The same five states with the largest degree centrality also have the largest eigenvector centralities. Figure 12 (c) shows the betweenness centrality of the states in the network. Betweenness centrality measures the number of times a node lies on the shortest path connecting other nodes. This identifies nodes that are “bridges” in the network, by counting the number of times a node is located on all the shortest paths. Nodes with high betweenness may influence flow around the system, hold authority over disparate clusters, or be on the periphery of both clusters. In this network, Illinois, Pennsylvania, the District of Columbia, Oregon, and Minnesota have particularly high values of betweenness. Figure 12 (d) shows the closeness centrality of all the states. Closeness centrality measures how many steps to reach every other node from a given node, or the average path length. It shows nodes who can influence the entire network most quickly or “broadcasters.” Since we see most nodes have a similar score, this is evidence that the network is highly connected. States with high betweenness values also have high closeness values. Arizona and Virginia have low closeness values, but they each had two attorney generals of different political party affiliation.
| Attorney Name | Role | Organization | Political Party | Degree Centrality | Eigenvector Centrality |
|---|---|---|---|---|---|
| Terry A Doughty | Distict Court Judge | Western District of Louisiana | Republican | 177 | 0.14 |
| Daniel L Hovland | District Court Judge | District of North Dakota | Republican | 119 | 0.09 |
| Drew B Tipton | District Court Judge | Southern District of Texas | Republican | 93 | 0.07 |
| Matthew J Kacsmaryk | District Court Judge | Northern District of Texas | Republican | 85 | 0.06 |
| Robert R Summerhays | District Court Judge | Western District of Louisiana | Republican | 58 | 0.05 |
| Travis R Mcdonough | District Court Judge | Eastern District of Tennessee | Democrat | 56 | 0.05 |
| Jeffrey V Brown | District Court Judge | Southern District of Texas | Republican | 53 | 0.05 |
| William F Jung | District Court Judge | Middle District of Florida | Republican | 51 | 0.05 |
| Charles E Atchley | District Court Judge | Eastern District of Tennessee | Republican | 51 | 0.05 |
| David C Joseph | District Court Judge | Western District of Louisiana | Republican | 49 | 0.05 |
| James Donato | District Court Judge | Northern District of California | Democrat | 45 | 0.00 |
| Daniel M Traynor | District Court Judge | District of North Dakota | Republican | 44 | 0.03 |
| Sri Srinvasan | Circuit Court Judge | DC Circuit Court of Appeals | Democrat | 41 | 0.04 |
| Gregory Katsas | Circuit Court Judge | DC Circuit Court of Appeals | Republican | 41 | 0.04 |
| Florence Y Pan | Circuit Court Judge | DC Circuit Court of Appeals | Democrat | 41 | 0.04 |
| Peter D Welte | District Court Judge | District of North Dakota | Republican | 41 | 0.04 |
| Sidney H Stein | District Court Judge | Southern District of New York | Democrat | 39 | 0.00 |
| Barbara Mg Lynn | District Court Judge | Northern District of Texas | Democrat | 37 | 0.03 |
| L Scott Coogler | District Court Judge | Northern District of Alabama | Republican | 36 | 0.03 |
| Jane Magnusstinson | District Court Judge | Southern District of Indiana | Democrat | 35 | 0.03 |
| James D Cain | District Court Judge | Western District of Louisiana | Republican | 32 | 0.02 |
| Thomas O Rice | District Court Judge | Eastern District of Washington | Democrat | 31 | 0.00 |
| Timothy S Black | District Court Judge | Southern District of Ohio | Democrat | 29 | 0.03 |
| Audrey G Fleissig | District Court Judge | Eastern District of Missouri | Democrat | 29 | 0.03 |
| Darrel J Papillion | District Court Judge | Eastern District of Louisiana | Democrat | 28 | 0.02 |
| Joseph S Dueker | Magistrate Judge | Eastern District of Missouri | Unknown | 25 | 0.02 |
| R Stan Baker | District Court Judge | Southern District of Georgia | Republican | 24 | 0.01 |
| Matthew T Schelp | District Court Judge | Eastern District of Missouri | Republican | 23 | 0.02 |
| Gregory F Van Tatenhove | District Court Judge | Eastern District of Kentucky | Republican | 22 | 0.01 |
| Halil S Ozerden | District Court Judge | Southern District of Mississippi | Republican | 18 | 0.02 |
| Dee D Drell | District Court Judge | Western District of Louisiana | Republican | 14 | 0.01 |
| Henry E Autrey | District Court Judge | Eastern District of Missouri | Republican | 14 | 0.01 |
| Terry R Means | District Court Judge | Northern District of Texas | Republican | 11 | 0.00 |
| John J Tuchi | District Court Judge | District of Arizona | Democrat | 11 | 0.01 |
| Michael J Newman | District Court Judge | Southern District of Ohio | Republican | 10 | 0.01 |
| Micaela Alvarez | District Court Judge | Southern District of Texas | Republican | 9 | 0.01 |
| Steven D Merryday | District Court Judge | Middle District of Florida | Republican | 9 | 0.00 |
| Susan R Bolton | District Court Judge | District of Arizona | Democrat | 8 | 0.01 |
| Corey L Maze | District Court Judge | Northern District of Alabama | Republican | 6 | 0.01 |
| Joseph M Hood | District Court Judge | Eastern District of Kentucky | Republican | 6 | 0.00 |
Table 1 lists the district court and magistrate judges in their organization with their respective political party affiliations, degree centrality, and eigenvector centrality. The network includes 40 judges serving across 19 districts. The judge with the highest degree and eigenvector centrality values is Terry A. Doughty, a Republican judge in the Western District of Louisiana, significantly surpassing other judges. Other notable districts with central judges comprise the District of North Dakota, the Southern and Northern Districts of Texas, and the Eastern District of Tennessee. The Western District of Louisiana features three of the most central judges within the network.
Figure 13 shows the network of judges and attorneys. The edge sizes in the graph are weighted by the number of interactions between each set of two nodes. The graph depicts two distinct clusters, which are largely related to the political party of the litigators. Attorneys are more central than judges. This is likely because attorneys are more often repeat players than judges in these multistate cases. This network has a degree assortativity of 0.21, indicating a slight preference for attorneys and judges with similar degree centrality to connect with each other. The assortativity by political party is 0.9439717, not as extreme as observed in the state network graph, it remains substantial. Additionally, the network assortativity value based on judge or attorney status, the network assortativity value is -0.0158807, slightly disassortative and implying mixing between attorneys and judges.
We have provided four interactive renditions of the litigator network, accessible through Figure 14, Figure 15, Figure 16, and Figure 17. Users can avail such features as rotation, panning, zooming, clicking, dragging, and node selection to enhance their network visualization experience.
Figure 18 summarizes the centrality measures for the most common, where the number of individuals holding the role is greater than five, by political party status. These distributions are largely positively skewed. The roles with the largest mean degree centrality are the Attorney and Solicitor General, followed by the deputies for each position and then assistants, and lastly district court judge.
Next, we address the grouping of states into districts. Specifically, is there a transition observed between using a larger band of states versus broken up into smaller bands in different districts?
Figure 19 shows the relationship of the filing date and the number of attorney generals. We do not see a clear trend.
Methods Discussion
This paper introduced a novel framework for analyzing the interactions existing between states and between the legal practitioners involved in multistate attorney general litigation. We created two distinct networks of the states and the litigators involved. These networks revealed two prominent clusters, largely corresponding to the political affiliations of the entities. We analyzed the networks for centrality to identify the central players in the litigation cases. Furthermore, our examination of the interaction of states within districts did not reveal any relevant shifts in how states band together.
Appendix
The network represented in Figure 22 depicts the connections among the litigation targets engaged in multistate litigation. Characterized by a core-periphery structure, this network exhibits loosely connected peripheral nodes surrounding a cohesive core. The central figure in this network is the President.
The interaction between plaintiff states and the litigation targets is visualized in Figure 23. The network consists of two distinct types of nodes, defendants and plaintiffs, engaged together in legal cases.
Computational Details
The following computational software and packages were used in the analysis: R version 4.3.0 (2023-04-21 ucrt), dplyr, ggplot2, GGally, kableExtra, igraph, readxl, stringr, scales, networkD3, threejs, htmlwidgets, visNetwork, plotly, maps, assertthat, purrr, ggraph, usmap, and ggmap. Quarto and VS Code were used for document compilation.
References
Afsharipour, Afra, Kristina Bishop, and Matthew Jennejohn. 2023. “Client Pressure and Persistent Diversity Gaps in the Courtroom.”
Afsharipour, Afra, and Matthew Jennejohn. 2022. “Gender and the Social Structure of Exclusion in U.S. Corporate Law.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4262079.
Ahern, Kenneth R. 2017. “Information Networks: Evidence from Illegal Insider Trading Tips.” Journal of Financial Economics 125 (1): 26–47. https://doi.org/10.1016/j.jfineco.2017.03.009.
Allaire, J. J., Christophe Dervieux, Carlos Scheidegger, Charles Teague, and Yihui Xie. 2022. Quarto (version 0.3). https://doi.org/10.5281/zenodo.5960048.
Allaire, J. J., Christopher Gandrud, Kenton Russell, and CJ Yetman. 2017. networkD3: D3 JavaScript Network Graphs from r. https://CRAN.R-project.org/package=networkD3.
Almende B.V. and Contributors, and Benoit Thieurmel. 2022. visNetwork: Network Visualization Using ’Vis.js’ Library. https://CRAN.R-project.org/package=visNetwork.
Badawi, Adam B., and Giuseppi Dari-Mattiacci. 2019. Law as Data. The Santa Fe Institute Press. https://www.sfipress.org/reference-networks-and-civil-codes.
Beaverstock, Jonathan V. 2004. “’Managing Across Borders’: Knowledge Management and Expatriation in Professional Service Legal Firms.” Journal of Economic Geography 4 (2): 157–79. https://www.jstor.org/stable/26160520.
Bernstein, Lisa. 2016. “Beyond Relational Contracts: Social Capital and Network Governance in Procurement Contracts.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=2711841.
———. 2018. “Contract Governance in Small World Networks: The Case of the Maghribi Traders.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://doi.org/10.2139/ssrn.3278003.
Bishop, Kristina, Matthew Jennejohn, and Cree Jones. 2022. “Top Ups and ’Telephone’.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://doi.org/10.2139/ssrn.4313301.
Borgatti, Stephen P., Ajay Mehra, Daniel J. Brass, and Giuseppe Labianca. 2009. “Network Analysis in the Social Sciences.” Science (New York, N.Y.) 323 (5916): 892–95. https://doi.org/10.1126/science.1165821.
Caldarelli, Guido, and Michele Catanzaro. 2012. Networks: A Very Short Introduction. Oxford Academic. https://doi.org/10.1093/actrade/9780199588077.001.0001.
Csardi, Gabor, and Tamas Nepusz. 2006. “The Igraph Software Package for Complex Network Research.” InterJournal Complex Systems: 1695. https://igraph.org.
Di Lorenzo, Paolo. 2023. Usmap: US Maps Including Alaska and Hawaii. https://CRAN.R-project.org/package=usmap.
Enriques, Luca, and Alessandro Romano. 2018. “Institutional Investor Voting Behavior: A Network Theory Perspective.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://doi.org/10.2139/ssrn.3157708.
Fowler, James H., Timothy R. Johnson, James F. Spriggs, Sangick Jeon, and Paul J. Wahlbeck. 2007. “Network Analysis and the Law: Measuring the Legal Importance of Precedents at the U.S. Supreme Court.” Political Analysis 15 (3): 324–46. https://doi.org/10.1093/pan/mpm011.
Gelter, Martin, and Mathias Siems. 2010. “Language, Legal Origins, and Culture Before the Courts: Cross-Citations Between Supreme Courts in Europe.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=1719183.
Grossetti, Michel, and Emmanuel Lazega. 2003. “The Collegial Phenomenon. The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership.” Revue Française de Sociologie 44 (January): 186. https://doi.org/10.2307/3323128.
Heinz, John P., Robert L. Nelson, Rebecca L. Sandefur, and Edward O. Laumann. 2005. Urban Lawyers: The New Social Structure of the Bar. Chicago, IL: University of Chicago Press. https://press.uchicago.edu/ucp/books/book/chicago/U/bo3534372.html.
Jennejohn, Matthew. 2015. “The Private Order of Innovation Networks.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=2680488.
———. 2022. “Do Networks Govern Contracts?” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=4086909.
Kahle, David, and Hadley Wickham. 2013. “Ggmap: Spatial Visualization with Ggplot2.” The R Journal 5 (1): 144–61. https://journal.r-project.org/archive/2013-1/kahle-wickham.pdf.
Katz, Daniel Martin, and Derek K. Stafford. 2008. “Hustle and Flow: A Social Network Analysis of the American Federal Judiciary.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=1103573.
Kraatz, Matthew S., and Nina Shah. 2003. “Review of The Collegial Phenomenon: The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership.” Administrative Science Quarterly 48 (3): 525–29. https://doi.org/10.2307/3556688.
Lazega, Emmanuel, and Marijtje van Duijn. 1997. “Position in Formal Structure, Personal Characteristics and Choices of Advisors in a Law Firm: A Logistic Regression Model for Dyadic Network Data.” Social Networks 19 (4): 375–97. https://doi.org/10.1016/S0378-8733(97)00006-3.
Lazega, Emmanuel, and David Krackhardt. 2000. “Spreading and Shifting Costs of Lateral Control Among Peers: A Structural Analysis at the Individual Level.” Quality and Quantity 34 (2): 153–75. https://doi.org/10.1023/A:1004759418226.
Lewis, B. W. 2020. Threejs: Interactive 3D Scatter Plots, Networks and Globes. https://CRAN.R-project.org/package=threejs.
Lior, Anat. 2020. “The AI Accident Network: Artificial Intelligence Liability Meets Network Theory.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=3561948.
Newman, M. E. J. 2003. “The Structure and Function of Complex Networks.” SIAM Review 45 (2): 167–256. https://doi.org/10.1137/S003614450342480.
Passador, Maria Lucia, and Alessandro Romano. 2022. “Why Legal Scholars Should Study Network Theory.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4044934.
Pedersen, Thomas Lin. 2022. Ggraph: An Implementation of Grammar of Graphics for Graphs and Networks. https://CRAN.R-project.org/package=ggraph.
Pedraza-Fariña, Laura, and Ryan Whalen. 2020. “A Network Theory of Patentability.” University of Chicago Law Review 87 (1). https://chicagounbound.uchicago.edu/uclrev/vol87/iss1/2.
Pelc, Krzysztof J. 2014. “The Politics of Precedent in International Law: A Social Network Application.” The American Political Science Review 108 (3): 547–64. https://www.jstor.org/stable/43654392.
Porat, Ariel, and Robert E. Scott. 2017. “Can Restitution Save Fragile Spiderless Networks?” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=2946510.
R Core Team. 2022. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Richard A. Becker, Original S code by, Allan R. Wilks. R version by Ray Brownrigg. Enhancements by Thomas P Minka, and Alex Deckmyn. 2022. Maps: Draw Geographical Maps. https://CRAN.R-project.org/package=maps.
Romano, Alessandro. 2018. “Horizontal Shareholding and Network Theory.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://doi.org/10.2139/ssrn.3255948.
Romano, Alessandro, Luca Enriques, and Jonathan R. Macey. 2019. “Extended Shareholder Liability for Systemically Important Financial Institutions.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://doi.org/10.2139/ssrn.3475828.
Schloerke, Barret, Di Cook, Joseph Larmarange, Francois Briatte, Moritz Marbach, Edwin Thoen, Amos Elberg, and Jason Crowley. 2021. GGally: Extension to ’Ggplot2’. https://CRAN.R-project.org/package=GGally.
Schwartz, Alan, and Robert E. Scott. 2015. “Third Party Beneficiaries and Contractual Networks.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://doi.org/10.2139/ssrn.2550436.
Sievert, Carson. 2020. Interactive Web-Based Data Visualization with r, Plotly, and Shiny. Chapman; Hall/CRC. https://plotly-r.com.
Vaidyanathan, Ramnath, Yihui Xie, JJ Allaire, Joe Cheng, Carson Sievert, and Kenton Russell. 2023. Htmlwidgets: HTML Widgets for r. https://CRAN.R-project.org/package=htmlwidgets.
Whalen, Ryan. 2016. “Legal Networks: The Promises and Challenges of Legal Network Analysis.” {SSRN} {Scholarly} {Paper}. Rochester, NY. https://papers.ssrn.com/abstract=3000144.
Wickham, Hadley. 2016. Ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org.
———. 2019. Assertthat: Easy Pre and Post Assertions. https://CRAN.R-project.org/package=assertthat.
———. 2022. Stringr: Simple, Consistent Wrappers for Common String Operations. https://CRAN.R-project.org/package=stringr.
Wickham, Hadley, and Jennifer Bryan. 2022. Readxl: Read Excel Files. https://CRAN.R-project.org/package=readxl.
Wickham, Hadley, Romain François, Lionel Henry, and Kirill Müller. 2022. Dplyr: A Grammar of Data Manipulation. https://CRAN.R-project.org/package=dplyr.
Wickham, Hadley, and Lionel Henry. 2023. Purrr: Functional Programming Tools. https://CRAN.R-project.org/package=purrr.
Wickham, Hadley, and Dana Seidel. 2022. Scales: Scale Functions for Visualization. https://CRAN.R-project.org/package=scales.
Zhu, Hao. 2021. kableExtra: Construct Complex Table with ’Kable’ and Pipe Syntax. https://CRAN.R-project.org/package=kableExtra.
Footnotes
Borgatti et al. (2009), Caldarelli and Catanzaro (2012), and Jackson (2008)↩︎
Passador and Romano (2022) argue that legal scholars should study network theory because social structures and interconnections among individuals shape our society. McClane and Nili (2019) posit that the structure of networks matters as much, or more than the direct connections, and examine the importance of director networks on corporate governance. See Whalen (2016) for a review of legal network analysis.↩︎
See, Fowler et al. (2007), Badawi and Dari-Mattiacci (2019), Gelter and Siems (2010), Katz and Stafford (2008), and Pelc (2014).↩︎
Schwartz and Scott (2015), Jennejohn (2015), Porat and Scott (2017), Bernstein (2016), Bernstein (2018), and Jennejohn (2022).↩︎
Lazega and Duijn (1997), Lazega and Krackhardt (2000), Kraatz and Shah (2003), Grossetti and Lazega (2003), Beaverstock (2004), and Heinz et al. (2005)↩︎
Afsharipour and Jennejohn (2022) and Afsharipour, Bishop, and Jennejohn (2023) model the gender and social structure in U.S. corporate law.↩︎
See Newman (2003) and Jackson (2008) for thorough expositions of network analysis.↩︎