Introduction: The Death of Stalin: A Social Network Analysis Study

Can we predict sucession of power in a network based on centrailty measures?

In this network study, we take the characters from the Armando Iannucci film, The Death of Stalin, a satirical dark comedy that reenacts the days immediately after the death of Stalin and the vacuum for power. Stalin intentionally did not have a succession plan in place, leaving his inner circle to chaotically determine who was the rightful next-in-line for control of the Soviet state.

Historically we know that after the death of Stalin, Georgy Malenkov took control for a short period of time, followed by Nikita Khrushchev. But not without meddling by Lavrenti Beria, which eventually lead to his unceremonious death.

In this study, we will use topographical and centrality measures to determine characteristics of the network and the individual characters before and after the removal of key players. By identifying key characters using statistical methods, we hope to evaluate the effectiveness of social network analysis in predicting the next successor to the Kremlin oligarchy.

Figure 1: The Death of Stalin Movie Network

The Death of Stalin Movie Network was created by cataloging any characters that had speaking roles and any interactions together that resulted in the transmission of information (including forms such as letter writing). There are 34 characters represented in this moderately centralized network are broken into four groups by community: The Bolsheviks, the Red Army, the NKVD (an abbreviation for The People’s Commissariat for Internal Affairs, or the Soviet secret police), or None (no direct affiliation to the other three groups).

The size of each character’s node is based on their degree within the network, or the number of connects the node has within the network. Intuitively, the more people you know, the more important you probably are within a network. Degree can be understood as direct power or influence, or the ability to influence another node due to proximity and access. Although this should be caveated because in some cases (and likely in this one), nodes can appear more well-connected than they actually are due to biased collection.

The Network: Topographical Measures

Network topography is used to describe the overall structure of a social network, allowing us to understand the strengths and vulnerabilities. Network structures differ depending on the type of network. A dark or covert network may rely on uncentralized network structure, depending on brokers of information to facilitate the flow of information. More traditional networks with strong command and control like a government or military, the type that we see in The Death of Stalin, relies on a centralized directorate and the ability to broker information to far flung sections of the network.

Topographical measures can help determine characteristics about the network. For example, how interconnected the Death of Stalin Network is, how centralized the network is, and if the network is dominated by a few individuals- or relatively egalitarian.

Below are descriptions of the different topographical measures used and their relevance to evaluating a network:

Diameter: The measure of the longest distance from node to node, while still taking the shortest path.

Average Path Length: The average shortest path for each node to get to its farthest counterpart in the network.

Average Degree: The average number of degrees that the nodes have, also known as the average number of connections each individual has.

Centralization: This indicates how centralized or decentralized, a network is. A network with a high degree of centralization can indicate that one or a few actors are relatively active compared to the rest of the actors.

Eigenvector Centralization: This measure indicates the level of which the network is dominated by a few actors. A higher eigenvector score insinuates that the network is more dominated, with a lower score being interpreted as less dominated.

Table 1: Topographical Measures

In this network, we are seeing a moderately centralized network that is being dominated by one or more individuals. This network is indicative of a traditional hierarchical structure.

Determining the Network’s Cut-Points

Figure 2: The Death of Stalin Movie Network, Cut-Points A cut-point (or articulation point) is the point within an undirected graph that can divide the graph into further components if the point is removed. Described more simply, the cut-point is an individual who can divide the group- this is important as they can identify critical positions of flow in a network since their removal by definition alters the connectivity properties of the graph.

In Figure 2, Lavrenti Beria, Vasily Stalin, Nikita Khrushchev, Georgy Malenkov, Field Marshal Zhukov, NKVD Officer Delov, and the Radio Producer all serve as cut-points. Some of these, such as NKVD Officer Delov and the Radio Producer can likely be explained due to their already peripheral status in the movie cast. They serve as links to other communities. But individuals like Lavrenti Beria and Nikita Khrushchev and Georgy Malenkov- all members of the inside circle, show that the trop of the heavily clique oriented Kremlin is true. Important individuals in the Kremlin have positioned themselves as points that can help facilitate (or hinder) information flow to maintain usefulness.

The Presence of Subgroups

Figure 3: Subgroups of The Death of Stalin Movie Network

This visualization draws attention to the different cohesive subgroups in network. Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent, or positive ties. These are the individuals that associate regularly in the movie- whether by work, shared communities, friendship, or otherwise. One of the most intuitive communities highlighted contains the Concert Director, the Radio Producer, and Sergei- all of whom share a working relationship at the concert hall.

The Characters: Node Centrality Scores

To identify and understand the key individuals in the network, we will use centrality measures to determine each nodes’: degree, betweenness, and eigenvector, and closeness. Each can be defined as:

Degree: Degree is the measure of the total number of edges (relationships) connected to a particular vertex (or person). Degree centrality is the simplest measure of centrality, and can be used to measure how many relationships a particular person has within the network. Degree centrality is useful for finding very connected individuals, popular individuals, individuals who are likely to hold most information or individuals who can quickly connect with the wider network

Betweenness: Betweenness centrality measures the number of times a node lies on the shortest path between other nodes. Betweenness is useful for analyzing communication dynamics, but should be used with care. A high betweenness count could indicate someone holds authority over disparate clusters in a network, or just that they are on the periphery of both clusters. Betweenness centrality is useful for finding the individuals who influence the flow around a system.

Eigenvector: Eigenvector centrality measures a node’s influence based on the number of links it has to other nodes in the network. Eigenvector centrality then goes a step further by also taking into account how well connected a node is, and how many links their connections have, and so on through the network. By calculating the extended connections of a node, Eigenvector centrality can identify nodes with influence over the whole network, not just those directly connected to that particular node.

Closeness: Closeness centrality scores each node based on their ‘closeness’ to all other nodes in the network. Closeness centrality can help find good ‘broadcasters’, but in a highly-connected network, you will often find all nodes have a similar score. Closeness is useful for finding the individuals who are best placed to influence the entire network most quickly.

Table 2: Death of Stalin Movie Network, Character Centrality

Above we find the centrality measures for each character in The Death of Stalin Movie Network. Centrality measures can help identify the popular characters, the characters who hold large amounts of power or influence over the network, and a character’s ability to disseminate information. These measures are closely related to each other, and multiple should be used to develop a well-rounded picture of a character and their role in the network.

In this first iteration of the network, Josef Stalin is still present, but relatively low ranking character across the board. This is likely due, at least partially, to his limited screen-time. Sometimes powerful individuals have low degree scores but high eigenvector scores- think of a politician, they don’t necessarily know very many people but many people know them and are influenced by them. In the case of Stalin, he has a relatively low eigenvector score compared to some other characters- meaning he isn’t relatively known or influential in this case.

The network is primarily controlled by Lavrenti Beria, Nikita Khrushchev, Georgy Malenkov; members of Stalin’s inner circle, it is easy to infer that they would be in the running to take control of the network after the death of Stalin.

Figure 3:The Death of Stalin Movie Network, Removal of Stalin

Here we have the group after the removal of Stalin. Stalin was not a cut-point, therefore nobody has been cut out of the group yet. To understand any changes to the network, it is important to revisit the topographical measures of the network, which can be seen below in Table 3.

Topographical Measures

Table 3: Topographical Measures, Removal of Stalin

After the removal of Stalin, the network actually stays relatively stable. There is a slight decrease in centralization which is understandable as a character was removed without a replacement. But otherwise the network stays relatively intact.

Node Centrality Scores

Table 4: Death of Stalin Movie Network, Character Centrality, Removal of Stalin

With the removal of Stalin, we don’t actually see many changes. This shouldn’t be very surprising as it was determined that Stalin isn’t a huge player in this network. Although we do see an increase of betweennes for Lavrenti Beria. In this case, we would expect that Beria would take control of the network and Khrushchev would be 2nd in line.

The Removal of Stalin and Beria

Figure 4: Figure 3:The Death of Stalin Movie Network, Removal of Stalin and Beria

The removal of Lavrentia Beria we see a more interesting shift in the network. Recalling that Beria was a cut-point, three individuals in the network have been disconnected from the main component: NKVD Officer Sliminov, Khrustalyov, Matryona Petrovna. For these individuals, Beria was a means of information flow, and vice versa.

The network is generally still connected, but should be examined by topographical measures to fully understand the extent that Beria’s departure changes the network.

Topographical Measures

Table 5: Topographical Measures, Removal of Stalin and Beria

Here we see more substantial changes to the network. The overall centralization of the network has decreased, while the eigenvector centralization has increased. The network has generally become less central, but the level of domination that specific characters have over the network has increased. As we see below when evaluating the character centrality, Nikita Khrushchev takes over a position of power within the network and centralizes power.

Table 6: Death of Stalin Movie Network, Character Centrality, Removal of Stalin and Beria

As one would expect, Nikita Khrushchev takes control of the network- which happens to be factually correct and aligns with history. The death of Stalin lead to the Khrushchev era in Soviet history.

Comparing the Networks

To fully understand the differences in the networks, it is important to compare the three networks against each other.

Table 7: Comparing the Three Networks

It is expected that as the network is parsed apart that the centralization of the network would diminish- which is demonstrated by a decrease in diameter, average path length, and degree centralization.

But interestingly enough, the Eigenvector Centralization increases over the different iterations- meaning that one character begins to control more and more of the network. Furthermore, the Average Degree increases- meaning that the average number of people that are known by the characters is increasing. The network is reorganizing into a different format than before to account for the removal of key characters.

Conclusion:

Power is reflected in different forms within a network, but using topographical measures and character centrality scores, one can infer the type of network and power present to determine the future controlling powers. Different types of networks present in different formats- with traditional hierarchical networks with strong command and control relying on traditionally conceived centrality, and covert networks depending on cells or more defrayed methods of information transmission- the type of network is equally as important as looking at traditional measures of examining individual nodes for their centrality scores. Power must be examined with nuance.