The world is a connected place, literally and figuratively. The field of network science is now used to understand phenomena as diverse as the spread of misinformation, West African trade, and protein-protein interactions in cells.
Network science has uncovered several universal properties of complex social networks, which in turn have made it possible to learn the details of specific networks. For example, the network that makes up the international financial corruption system uncovered by the Panama Papers investigation exhibits an unusual lack of connections between its parts.
But understanding the hidden structures of key elements of social networks, such as subgroups, has remained elusive. My colleagues and I have found two complex patterns in these networks that can help researchers better understand the hierarchies and dynamics of these elements. We found a way to spot powerful “inner circles” in large organizations simply by examining networks that map emails sent between employees.
We demonstrated the utility of our methods by applying them to the famous Enron network. Enron was an energy trading company that committed fraud on a large scale. Our study also showed that the method can potentially be used to identify individuals who have tremendous soft power, regardless of their official title or position in an organization. This could be useful for historical, sociological, economic, governmental, legal, and media research.
From pencil and paper to artificial intelligence
Sociologists have been constructing and studying smaller social networks in careful field experiments for at least 80 years, well before the advent of the Internet and online social networks. The concept is simple enough to draw on paper: entities of interest – people, companies, countries – are nodes represented as dots, and relationships between pairs of nodes are connections represented as lines between the dots.
Using network science to study human societies and other complex systems took on new meaning in the late 1990s, when researchers discovered some universal properties of networks. Some of these universal qualities have now entered mainstream pop culture. One concept is Kevin Bacon’s Six Degrees, based on the famous empirical finding that any two people on Earth are six links or less apart. Similarly, versions of statements such as “the rich get richer” and “the winner takes all” have been replicated on some networks.
These global properties, valid for the entire network, seem to emerge from the myopic and local actions of independent nodes. When I connect with someone on LinkedIn, I certainly don’t think about the global implications of my connection on the LinkedIn network. Yet my actions, along with those of many others, eventually lead to predictable, rather than random, outcomes about how the network will evolve.
My colleagues and I have used network science to study human trafficking in the UK, the structure of noise in artificial intelligence system outputs, and financial corruption in the Panama Papers.
Groups have their own structure
In addition to studying new properties like Kevin Bacon’s Six Degrees, researchers have also used network science to focus on problems like community detection. Put simply, can a set of rules, also known as an algorithm, automatically discover groups or communities within a collection of people?
Today there are hundreds if not thousands of community detection algorithms, some of which rely on advanced AI methods. They are used for many purposes, including finding communities of interest and exposing malicious groups on social media. Such algorithms encode intuitive assumptions, such as the expectation that nodes belonging to the same group are more closely connected than nodes belonging to different groups.
While exciting work, community detection does not examine the internal structure of communities. Should communities only be viewed as collections of nodes in networks? And what about communities that are small but particularly influential, like inner circles and in-crowds?
Two hypothetical structures for influential groups
You probably already have an idea, so to speak, of the structure of very small groups in social networks. The truth of the saying “a friend of my friend is my friend” can be tested statistically in friendship networks by counting the number of triangles in the network and determining if that number is higher than chance alone could explain. Indeed, many social media studies have been used to verify this claim.
Unfortunately, the concept breaks down when extended to groups with more than three members. Although motifs have been well studied in both algorithmic computer science and biology, they have not been reliably linked to influential groups in real-world communication networks.
Building on this tradition, my graduate student Ke Shen and I have found and presented two structures that appear elaborate but turn out to be quite common in real-world networks.
The first structure does not extend the triangle by adding more nodes, but by adding triangles directly. In particular, there is a central triangle flanked by other peripheral triangles. Importantly, the third person in a peripheral triangle must not be connected to the third person in the central triangle, thereby excluding them from the true inner circle of influence.
The second structure is similar but assumes there is no central triangle and the inner circle is just a pair of nodes. A real-life example might be two startup co-founders like Sergey Brin and Google’s Larry Page, or a power couple with common interests common in world politics, like Bill and Hillary Clinton.
Understand influential groups in a notorious network
We tested our hypothesis on the Enron email network, well studied in network science, with nodes representing email addresses and links representing communications between those addresses. Although our proposed structures were detailed, not only were they present in the network in greater numbers than chance alone would predict, but qualitative analysis showed that the claim that they represent influential groups is valid.
The main characters of the Enron saga are now well documented. Intriguingly, some of these characters don’t appear to have had much official influence, but may have exercised significant soft power. One example is Sherri Reinartz-Sera, the longtime administrative assistant to Jeffrey K. Skilling, former Enron CEO. Unlike Skilling, Sera was only mentioned in a New York Times article following investigative reporting that took place during the course of the scandal. However, our algorithm has uncovered an influential group in which Sera holds a central position.
dissect power dynamics
Society has complicated structures at the level of individuals, friendships and communities. In-crowds aren’t just ragtag groups of characters talking to each other, or a single ringleader in charge. Many in-crowds or influential groups have an elaborate structure.
While much remains to be discovered about such groups and their influence, network science can help uncover their complexity.