Complex Societies and the Growth of the Law – Published Today in Scientific Reports (Nature Research)

Access the Full Article via Scientific Reports (Nature Research). This article is part of a special compilation for Scientific Reports devoted to Social Physics.

ABSTRACT: While many informal factors influence how people interact, modern societies rely upon law as a primary mechanism to formally control human behaviour. How legal rules impact societal development depends on the interplay between two types of actors: the people who create the rules and the people to which the rules potentially apply. We hypothesise that an increasingly diverse and interconnected society might create increasingly diverse and interconnected rules, and assert that legal networks provide a useful lens through which to observe the interaction between law and society. To evaluate these propositions, we present a novel and generalizable model of statutory materials as multidimensional, time-evolving document networks. Applying this model to the federal legislation of the United States and Germany, we find impressive expansion in the size and complexity of laws over the past two and a half decades. We investigate the sources of this development using methods from network science and natural language processing. To allow for cross-country comparisons over time, based on the explicit cross-references between legal rules, we algorithmically reorganise the legislative materials of the United States and Germany into cluster families that reflect legal topics. This reorganisation reveals that the main driver behind the growth of the law in both jurisdictions is the expansion of the welfare state, backed by an expansion of the tax state. Hence, our findings highlight the power of document network analysis for understanding the evolution of law and its relationship with society.

It has been a real pleasure to work with my transatlantic colleagues Corinna Coupette (Max Planck Institute for Informatics), Janis Beckedorf (Heidelberg University) and Dirk Hartung (Bucerius Law School). We have other projects also in the works — so stay tuned!

Dynamic Animation of the East Anglia Climate Research Unit Email Network



Click on this icon to view the Movie in Full Screen Mode!Picture 4


In our prior post analyzing the email database of Climate Research Unit at the University of East Anglia, we aggregated all emails over the relevant 1997-2009 time period into a single static visualization. Specifically, to build the network, we processed every email in the leaked data. Each email contains a sender and at least one recipient on the To:, Cc:, or Bcc: line.

One obvious shortcoming associated with producing a static snapshot for data set, is that it often obscures the time evolving dynamics of interaction which produced the full graph.  To generate a dynamic picture, it is necessary to collect time stamped network data. In the current case, this required acquisition of the date field for each of the emails. With this information, we used the same underlying data to generate a dynamic network animation for the 1997-2009 time window.


Consistent with the approach offered in our prior visualization, each node represents an individual within the email dataset while each connection reflects the weighted relationship between those individuals. The movie posted above features the date in the upper left.  As time ticks forward, you will notice that the relative social relationships between individuals are updated with each new batch of emails.  In some periods, this updating has significant impact upon the broader network topology and at other time it imposes little structural consequences.

In each period, both new connections as well as new communications across existing connections are colored teal while the existing and dormant relationships remain white.  Among other things, this is useful because it identifies when a connection is established and which interactions are active at any given time period.


We have two separate versions of the movie.  The version above is a shorter version where roughly 13 years is displayed in under 2 minutes.  In the coming days, we will have a longer version of the movie which ticks a one email at a time. In both versions, each frame is rendered using the Kamada-Kawai layout algorithm. Then, the frames are threaded together using linear interpolation.


Issues of selection of confront many researchers. Namely, given the released emails are only a subset of the broader universe of emails authored over the relevant time window, it is important to remember that the data has been filtered and the impact of this filtration can not be precisely determined. Notwithstanding this issue, our assumption is that every email from a sender to a recipient represents a some level of relationship between them.  Furthermore, we assume that more emails sent between two people generally indicates a stronger relationship between those individuals.


In our academic scholarship, we have confronted questions of dimensionality in network data. Simply put, analyzing network data drawn from high dimensional space can be really thorny. In the current context, a given email box likely contains emails on lots of subjects and reflects lots of people not relevant to the specific issue in question. Again, while we do not specifically know the manner in which the filter was applied, it is certainly possible that the filter actually served to mitigate issues of dimensionality.


For those interested in searching the emails, the NY Times directs the end user to

Visualizing Dynamic Networks with Python, Igraph, and SONIA

igraph2sonia Example 1 from michael bommarito on Vimeo.

When it comes to quickly motivating a point or engaging students in a classroom, one of the most effective tools is visualization. Not only do movies provide fun and excitement, but they also allow viewers to leverage the abilities of the visual cortex to infer dynamics and patterns in the animated system.

For our recent research, dynamic graphs are the type of system of interest. As I’ve covered before, Python is my language of choice for most programming tasks. Furthermore, Python is a very accessible language, even for beginners. However, when it comes to visualizing dynamic networks, we need another tool.  Our tool of choice is SONIA, the Social Network Image Animator.

I thought I’d provide a helpful little function to generate SONIA input files from igraph objects, along with a few examples.

This function takes as input an igraph.Graph object and a file name to store the SONIA output in. Every vertex in the Graph object should have a time attributed specified, either simply as an integer indicating the start time, or as a tuple or list of the form (startTime,endTime). Check out the following two examples if you need more guidance. Both examples visualize the construction of a periodic lattice. However, in the second example, nodes decay after some random time. Make sure not to miss the second video at the bottom of the post!

igraph2sonia Example 2 from Michael J Bommarito II on Vimeo.