In recent days, the number of revelations about connections between President Donald Trump and Russia have been expanding. The rate and identity of these connections have already caused one White House adviser to resign and the attorney general to recuse himself from further investigations. The story has been advancing so quickly that it’s difficult for even avid news consumers to keep track of the identities and type of connections between team Trump, his associates, and Russian government agents and businesses.

Of course, a president, his staff, or his Cabinet meeting with foreign leaders is not unusual. But in this context, it is. It’s important to remember that the intelligence services of the US government have concluded that Russia was involved with hacking the Democratic National Committee and interfering with the US 2016 election, which Trump won.

Recently, the Washington Post began mapping the connections between Trump and his affiliates and the Russians. This is a challenging task that, at this stage of limited public information, is nearly impossible to master. There is still more that we don’t know about these relationships than what we do know, and new information is coming out all the time. However, the Post’s efforts are worthy of recognition and encouragement because understanding the relationships between political actors helps us better understand their motivations and behaviors.

Mapping connections can provide insights

An entire academic field of political networks exists for this purpose. When our questions about politics are about relationships, or the connections between people, groups, and institutions, we need network methods to find answers. Applying non-relationship-based tools to questions that are about relationships results in incorrect conclusions. Moreover, the eagle-eye view provided by a whole network analysis can often provide insights that cannot be uncovered using a traditional analytical tool that focuses on individuals. Think of the clichéd crime investigator with clippings and notes on a cork board connected by pushpins and string. An approach like this can be useful in helping an analyst develop insights that are difficult to see otherwise.

Fortunately, advances in technology and methodology provide us with techniques that go well beyond the cork board. The Post made a good effort to piece together such an analysis with its graphic. However, there is room for improvement. For example, the layout of this graphic has been imposed by the designer. In other words, the Post wanted to show that Trump was at the top of this hierarchy, and so it placed him there. But it’s far better to use the strength of ties between the actors to show how “close” they are to one another.

The Post was careful to make a number of caveats, which also apply here. We do not have complete information about who is involved and how all the actors are connected to one another. In a technical sense, the models we can create have omitted actors, and we don’t know who they are. This missing data may be consequential, or it may not. If the missing actors and connections are highly important to drawing conclusions from the graph, then the incompleteness will be problematic.

For example, suppose there was evidence of direct contact between Trump and Putin — which, to be clear, no one is saying exists — but it if were true, and such a link were missing from the graph, we would not be able to draw accurate conclusions from the data. The omission of important actors or connections makes it nearly impossible to draw conclusions from the graph. Since we are certain we do not yet have all the actors and connections, we really cannot draw any conclusions. Still, there may be some utility in the exercise, and the data can be updated as new information becomes available — as it has, nearly every day.

Scholars have developed a series of best practices or rules to follow when displaying data of this type. Following these rules can help us gain insights into the network. The very first rule of creating a network map is to be thoughtful about layout. While some graphs look a bit like a mess of spaghetti, appropriate layout can reveal overall structure between relationships. It can help find cliques, factions, or communities.

It can also reveal which actors are most central to the network or to parts of the network. In politics, centrality is often associated with power. Graphing a network can help us check to see if the people we think are in power are actually central to the relationships in a network. Layout can also help us identify those who might act as brokers, or provide a bridge between two components that would otherwise be unconnected.

The principles of proper layout that can help us make these discoveries include the following. First, minimize crossing lines. When too many lines cross in a graph (as in the Post’s), it can be difficult to see structure or to visually follow the paths. Second, maximize angles. Too many acute angles make the graph tighter and denser, and contribute to complexity that may be unnecessary. Third, optimize line lengths and path distances. Actors that are more tightly connected in the network should appear closer together on the graph, and those who are not very well-connected should be farther apart. Computers use layout algorithms to achieve this effect.

Useful network graphs of the Trump-Russia connections

Applying these principles alone to the graph the Post produced makes the network look like this:

This graph is a rough sketch and is not as slick as the Post’s — for example, I didn’t use photographs for the nodes, which is a nice added visual — but the layout provides a more accurate depiction of the connections between the actors. Trump appears at the center of this graph in part because the data we are collecting is all about how all of these people are connected to Trump. He may be truly at the center of this network, but that may not mean very much about his role because we are in fact trying to determine how all of these people are connected to him.

The above graph also shows each node (or actor) as a circle that is sized proportionally to the actor’s centrality in the network. These nodes are sized by eigenvector centrality, which is a measure of centrality that takes into account how each actor is connected to every other actor in the network to show which are the most prominent.

We can improve this further by including some obvious additional connections. The Post’s graph for example, didn’t show Trump connected to Tillerson (his secretary of state) or his son Donald Trump Jr. The Post was not particularly careful about defining the relationships between these actors. In some cases, the connections are employer-employee, or business partners, or campaign co-workers, or simply that two people were known to have had conversations (such as with Russian Ambassador Sergey Kislyak).

For the purposes of this analysis, it seems okay to be somewhat liberal about these associations because we are simply using the graphing strategy to be somewhat exploratory about these connections. But we should keep in mind that they are not all equal. Future iterations may seek to be more exact about the strength and type of the relationships.

Reading through the Post’s careful write-up, we can add some additional meaningful actors and connections, and we can be deliberate about the direction of the connections. For example, we know that the Russian government was involved with hacking the DNC, which would indicate a connection from Russia to the DNC, but not the other way around.

Also, there are “nodes” on the graph that are not individuals but rather collections of individuals (e.g., Russian government and Russian business). It’s not typical to include two types of nodes in the same graph. It’s confusing to have some nodes as individual people and some nodes as groups. For example, Kislyak is clearly part of the Russian government. However, in this case, I think the Post (and I) are assuming that the nodes for Russian government and Russian business are stand-ins for individuals that are still unknown.

Adding in some of these connections makes the graph look like this:

The above graph is more complex than the previous, and it provides more information. While not as slick, it’s considerably more informative than the Post’s. The strength of the relationship between President Trump and Russian business is both central and prominent in this map. This happens because Trump and many of his associates have done business in Russia. It’s notable that the Russian government is much more closely tied to its economy and national business interests compared with the US. For instance, the Russian government has been heavy-handed in using government tools to develop regional dominance over access to oil and natural gas.

Additionally, we can ask the software to find “factions” or closely connected components within the graph. There is not much to go on (yet) with respect to finding distinct communities in the graph, but I suspect this approach may be more fruitful as more information becomes available.

Here you can see that there is one component (in blue) that includes the White House but also Russian business. The red (Russian) component includes the government and the actors it has most closely associated with, including the DNC via the hacking. The third component, in black, mostly appears to be made of those connected to foreign policy and diplomatic affairs. This analysis is exploratory and does not lead to any causal mechanisms or revelations, but as a descriptive analysis it helps us better understand the nature of the associations in this complex web.

The above graphs were produced in NetDraw, which is a user-friendly graphing software for networks. Importantly, the algorithm NetDraw uses lays out the nodes to reflect their level of closeness or connectivity. Other software uses slightly different algorithms and features. Gephi makes the graph look like this:

The graph created in Gephi is a bit more stylish, but has more crossing lines, making it harder to read, in my opinion. The size and color of each node indicates its centrality to the network, larger and darker being more central.

Ultimately, there is still much we don’t know about the relationship between Trump and Russia. As more information is revealed about more connections between Trump associates and Russians, the picture gets both murkier (because of complexity) and clearer (because of marginal transparency). So far there is no evidence of Trump’s direct involvement in anything illegal, but his denials and attempts to misdirect add to the air of suspicion around him.

Journalists and network scholars can help add to revealing relationships by investigating the extent of the connections between the myriad actors apparently involved in these complex scandals. Applying statistical tools and data visualizations to the complex web of relationships can help us better understand what’s happening.