This blog article is adapted from a paper presented at a 2012 conference for non-scientists who have declared that making a difference in the world is part of their life’s mission. It was an introduction to social network analysis and was meant to introduce them to new ways of analyzing social networks and examining how ideas flow through connected individuals (e.g., “going viral”).
In recent years, the hidden complexity of human interactions and information flow in our highly-connected society has attracted considerable attention from sociologists, economists, computer scientists, and applied mathematicians. Here, we introduce the discipline of Social Network Analysis (SNA) and examine its relevance to individuals wanting to make a difference in the world.
What is a Social Network Graph?
SNA uses a branch of mathematics known as graph theory to represent and visualize the hidden interactions between individuals in a community. We show an example graph in here. A graph consists of a set of nodes that are connected by links called edges. In the figure, nodes are represented as circles labeled with a capital letter. We refer to two nodes connected by a single edge as neighbors. Nodes A and B are neighbors because there is an edge that connects them. In the context of SNA, nodes are individuals and an edge indicates some level of interaction between the two neighbors. We will use the term actor to refer to the individual represented by a given node. The length of an edge in the figure does not have any meaning in this example. In this simple example, we do not indicate finer aspects of communication, such as strongly uni-directional communication (e.g., watching TV) and affinity for each other. These communication attributes can be encoded in various ways if needed.
There are a tremendous number of measures that scientists use (with names like betweenness, reach, and eigenvector centrality) to make SNA a quantitative tool. For simplicity, we will restrict ourselves to a mostly qualitative examination of few interesting network attributes. Interested readers are encouraged to research SNA to see how to use it for spreading their message(s).
The Strength of Weak Ties
Suppose you wanted to find a new job. Which people in your social circles would be most helpful? The answer may surprise you! Delving into this question provides an opportunity to see how SNA can help you identify unseen dynamics in your circle of friends, family, and associates, and can assist you in the spread of your messages.
We start first by identifying a key network feature. Consider again the network above. We say that the A-B edge is a local bridge because A and B have no neighbors in common. In the figure, A has C, D, E, and F as neighbors but B is not neighbors with any of them. Since A, C, D, E, and F form a tightly-knit group, they are likely to have the similar opinions and have access to the same information. Note, however, that the local bridge potentially allows B access to the information of this group through her relationship with A.
What do local bridges have to do with our job search question? As part of his Ph.D. research, Mark Granovetter found that most people who found a new job did so through acquaintances and not close friends. At first, this may seem counterintuitive. Wouldn’t your good friends be more likely to help you out than that Bob guy you talk with at the gym? Granovetter’s groundbreaking answer linked the “quality” of an interpersonal relationship to attributes of the network structure in a novel way.
One can characterize the quality of an interpersonal relationship, or tie, by labeling it as strong, weak, or nodding. Strong ties are those you enjoy with your close friends, family, trusted coworkers, etc. Weak ties are those you have with acquaintances who you interact with sporadically. Nodding ties represent insignificant verbal or nonverbal interactions, such as nodding “hello” to the lady who walks her dogs by your house every day.
Granovetter found that in many networks local bridges must necessarily be weak ties! These ties connect us to new sources of information, resources, and opportunities, such as job openings. Your close friends may have a strong desire to help you find a job, set you up on a date, and so forth; however, it is your weak ties where the new opportunities will come. From a network perspective, weak ties connect actors to hard-to-reach parts of the network. This is why sociologists refer to the “strength of weak ties”.
Granovetter submitted his findings to the American Sociological Review only to have his paper rejected. Undaunted, he then submitted it to the American Journal of Sociology, which accepted it. His paper has since become one of the most influential sociology papers of all time. Moral: don’t let a few early setbacks dissuade you from making your contribution to the world.
A’s weak tie to B provides him with new opportunities. What else does A’s position in the network lead to? Imagine that there is another node, Q, in the middle of the A, C, D, E group. Not only is Q friends with all of them, they are all friends with each other. We say that Q has a high clustering coefficient. Q’s interactions with any member of the group are safe, predictable, and typically positive, due to the threat of potentially being ostracized by common friends. For example, if E borrows money from Q and does not pay it back, A and D are sure to find out and look unfavorably on E. This can be a strong deterrent against any breach of integrity on E’s part.
Q is not part of a local bridge, but A is. A’s interactions with F are riskier since they only share one common friend, C. With weaker social pressures to enforce integrity, A may need to be more careful when dealing with F.
In addition, A may experience different and potentially conflicting opinions and values from his cliques. If A applies values from the C-D-E clique to help resolve a conflict between B and H, he runs the risk of his good friend B viewing him and his strange opinions as unwanted.
In both these situations, A’s position places him in more risky situations than someone with a high clustering coefficient. But A’s position in the network also confers certain advantages. Studies of the dynamics of large corporations have shown that the success of managers is correlated with their access to multiple local bridges. An actor in such a network position is said to span a structural hole in the network and has access to information from multiple, non-interacting sections. This position can foster creativity by enabling the combination of ideas in novel ways. Additionally, the actor regulates the flow of information between the non-interacting sections. When you are trying to start a movement, positioning yourself at a structural hole could enable you to facilitate the growth of your movement. As your movement grows, however, your continued presence at a structural hole limits what’s possible. Eventually, continued growth will require you to make strategic introductions among actors to forge sufficient links to close the hole and render yourself irrelevant.
We’ve seen a few examples of how network structure can influence what happens locally to individual actors. We turn our attention now to another use of SNA, namely, seeing how structure influences what happens in the network on a global level.
Information Cascades in Networks
So far we’ve simply looked at the point-to-point (e.g., local) transmission of information in a social network. Simple transmission does not necessarily result in a change in one’s actions. Can an examination of information flow assist us in understanding what might influence an individual to give up their beliefs and opinions and change their behaviors? When people take new actions due to the influence of others, sociologists say that herding behavior, or an information cascade, has occurred in the network. We will look at some of the issues involving the starting and stopping of information cascades in this section.
We will use an (overly simple) example here to demonstrate some concepts. Suppose you are sharing your vision and mission with someone you regularly interact with. Your friend is inspired by you and considering playing a role in helping your movement grow but has concerns. You are the only person among their friends and acquaintances doing this. If more people they knew would join your team, there is a much higher likelihood that they would join too. We’ll refer to them moving from simply being inspired to taking action as registration. Stated in network terms, there is a certain threshold fraction of neighbors that must have joined your movement before they will also join (i.e., register). If every actor in the network adopts this strategy for deciding whether to join, this may or may not result in a total cascade effect where everyone registers. It all depends on which node(s) register first, the threshold value, and the network structure.
Consider the network above. In this example, we will choose the “registration threshold” to be 2/5. That is, for any actor to register, 2/5 or more of his neighbors must have already registered. Let’s say you, Actor 7 in the figure, and your friend, Actor 8, start the cascade by registering in the movement. You (7) and 8 have five neighbors (4, 5, 9, 10, 14) but only 5 and 10 register at the next stage, due to the threshold value (e.g., 4 does not register because only 1/3 of her neighbors have registered). In the next step, Actors 4 and 9 register. In the third step, only Actor 6 registers. At this point, no other nodes will register because they don’t have enough neighbors who have also done so. We indicate those actors who have registered at the final stage by ovals with thicker borders.
Why did the cascade stop? In looking at the network, we can see that there are only local bridges between the 4, 5, 6, 7, 8, 9, 10 group of friends and the 11, 12, 13, 14, 15, 16, 17 group. If there was an edge between 10 and 11, actor 11 would then register since two of his four neighbors would have done so. But the cascade would still not restart since none of 11’s neighbors would register. Note also, that an edge between 9 and 12 would still not be enough to get 12 to register. If you want the cascade of registrations to restart, you would have to personally share your mission with 12 – a key actor in the network – to get things moving again.
Recall that we saw earlier that local bridges facilitate awareness of new ideas. It turns out, however, that these same bridges are weak at transmitting behaviors that actors deem risky. An actor at a bridge needs a higher threshold of neighbors to register before they do and the network structure of this example doesn’t support that. Research has shown historically that strong ties, rather than weak ties, are more significant for spreading activism, although it should be noted that much of this research was done before widespread adoption of the Internet. It is not clear whether this is still true for the spread of risky behaviors in the Internet Age.
What Happens When People Stop Talking To Each Other
There are many powerful techniques in SNA to discern hidden patterns. We turn our attention to a famous case study by Zachary of the social dynamics of a university karate club he was studying. At the start of the study, the club was a single, cohesive group of individuals but by the end, it had fractured into two rival clubs. What went wrong? Could SNA have identified problems before they reached the breaking point?
We display the social network of the karate club in the top of the figure to the right. Some nodes are shown as white circles and some as gray squares to show the two rival clubs that eventually formed. The edges here reflect interactions actors had with each other outside the club setting. From a close examination, we can see some signs of trouble. Actors 1 and 34 seem to be quite popular, with connections to many other club members, but there is no edge connecting them with each other. In reality, Actor 1 was the head instructor and 34 was the club president. The lack of an edge suggests they no attempt to resolve their differences through communication.
In the bottom of the figure, we display the same network in three pieces. This network was created by using the clusterMaker plugin for the open-source SNA software Cytoscape. The package provides several algorithms for detecting densely connected regions in a network. The algorithm we used for this example essentially focuses on identifying and removing edges that link densely connected regions. Once some links are removed, the network begins to break into pieces, which can then also be examined for sparse links.
Here, the algorithm predicted a fracture into three groups instead of two. While that is incorrect, it is interesting to note that it identified every actor that joined 34, with the exception of Actor 10. This type of analysis is not perfect. In fact, Zachary noted in his original analysis that one of the actors joined the group opposite of what his algorithm predicted because that individual was three weeks away from completing a four-year quest to obtain his black belt, which he could only do with the instructor. Such subtleties cannot be captured in the analysis. Nevertheless, the power to identify potential breakdowns in one’s social circle with a few clicks of a computer is an intriguing prospect.
Now What Will You Do With This Information?
You have made a promise to yourself to work to change the world. Congratulations! In a perfect world, you would share our vision freely with everyone in your life. In practice, however, it is a rare individual who does this because there is a great deal of negativity and cynicism in society. After reading this article, you may have new insights about who are the critical people in your circle of friends, family, and acquaintances to share with and ultimately register in your movement to create a cascade effect. And on a smaller scale, you may also be in a unique position to empower certain people in your life to step up and become leaders. When sharing your life’s mission with others, listen closely to their reactions. Some may give hints that they are secretly looking for an opportunity to play a bigger game in life but have not had the opportunity to do so. For those individuals who you suspect may have an interest in the creation of new ideas and/or fostering teamwork, a few strategic introductions (e.g., edge creation in the network) on your part to position them at local bridges could provide them with the opportunity to become the leader they always secretly hoped they would become. Do not let your passion in making a global difference blind you to the importance and fulfillment you may enjoy by assisting one of your friends in transforming their life as well.