We dive into the meat of the course this week by considering the essential elements of social network analysis. Although the analysis of a social network can become very complicated in its detail, at its core a social network offers perhaps the simplest possible vision of sociology, consisting of nothing more than the following two elements:
1. A node, something that communicates with other nodes, and
2. A tie, the path of communication between two nodes.
Everything having to do with social networks can be boiled down to descriptions of patterns in nodes and ties. Social network analysts have the audacity to claim that if you can describe patterns of nodes and ties in communication, you can understand our social world.
This week, we consider nodes, ties and the historical origin of ideas about nodes and ties in psychology, sociology, anthropology and mathematics — all thanks to a man in 18th century Prussia who didn’t want to cross a bridge twice.
As you read this lecture, read Chapter 2 of Christina Prell’s text Social Network Analysis: History, Theory and Methodology and Chapter 3 of Derek Hansen et al’s Analyzing Social Media Networks with NodeXL alongside. You may find it helpful to read a bit of lecture, then read a bit of text, then jump back to the lecture to reorient yourself.
Our lecture subjects this week are:
- Don’t Panic!
- Sorting Out Network Technology
- The Two Questions that Generate a Network
- Draw Me a Network!
- The Three Different Mainstream Ways to Represent a Network
- One-Mode and Two-Mode Networks
- Don’t Forget Homework
- Any Questions?
As you read your textbook, you may really be enjoying yourself. On the other hand, on a few pages you might start to feel a nasty, tickling sense creeping up your spine: the sense that you can’t possibly understand what you’re reading. Here’s my two-word piece of advice:
Don’t panic! The truth is that your textbooks are written to be read differently by people at many different stages of their education. Some parts of this week’s chapters should be pretty easy to understand, but some parts of them are written at a level I don’t expect you to understand (although you just might understand them perfectly, too). Let me set your mind at ease by describing a few sections of this week’s reading that I wouldn’t worry about too much:
- In Chapter 2 of Christina Prell’s text, pay attention to the broad strokes of the history of the development of social networks. Don’t worry too much about figuring out what technical terms like “n-clique” or “ERGMs” mean yet. We’ll return to some of these, like the “n-clique,” later on this semester.
- In the Hansen text, don’t worry too much about telling the difference between the different kinds of centrality (degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality). We’ll get to those distinctions later on in the semester. Consider pp. 40-41 to be a teaser and move on.
This is a 300-level course, and that means that we’re working with some high-level reading. It’s important for you to dive into this stuff, because once you graduate you should be fairly comfortable with reading at this level — but as an undergraduate I know that technical reading can be uncomfortable. Remind yourself that this is the discomfort of stretching yourself and growing as a learner, but also give yourself a break from time to time! As we head through the course, there will occasionally be passages that drive you mad. Put down the book, step away, get a drink of water, pick up the book and try again. If you just can’t understand a passage, post a comment to the relevant lecture or send me an e-mail message asking about it, and I’ll be glad to help clarify.
I’d like to know directly from the source — you — about how your experience in the class so far is going. How comfortable are you with the textbook readings? With the online lectures? With the syllabus? What’s going well and not so well for you? Here’s your chance to let me know — fill out this anonymous poll:
Thanks for letting me know. I’m always glad to hear if things are going well, but I’m especially glad when someone lets me know about a problem, because then we can start thinking about how to resolve it.
Sorting out Network Terminology
One of the features of a new field is that the language for describing that field hasn’t been completely sorted out. Because social network analysis is relatively new, people use a lot of synonyms to refer to the same idea. Learning those synonyms can be a bit of a headache, but it’s important if you want to be understand social network research.
The Prell and Hansen introductory chapters do a pretty good job of introducing the basic vocabulary of social networks, but there are a few points on which they’re a bit vague. Let’s review them here:
1. “Actors,” “Dots,” “Points,” “Nodes,” “Vertices,” “Agents,” and “Individuals” all refer to the same thing: the individual unit that does communicating in a social network.
2. “Arcs,” “Edges,” “Lines,” “Ties,” and “Connections” all refer to the same thing: the communication that happens in a social network. Most often, we just call these ties, but it’s important to know the synonyms.
There are two different kinds of ties: “directed” and “undirected.” Undirected ties have no arrowheads and occur when the connection being described has no particular direction between the two connected nodes. For instance, we might draw an edge between Node A and Node B if the connection between them is “has lunch together.”
On the other hand, directed ties have arrowheads indicating the direction of a relationship between two nodes. For instance, we might represent an arc from Node A to Node B by drawing an arrow originating with Node A and pointing to Node B, to represent the idea that Node A “likes” Node B or “shoots a spitball at” Node B.
3. In ego networks, egos are sometimes called “senders” and alters are sometimes called “receivers.” And to complicate matters a little, there are actually three kinds of ego networks:
4. A “relation” is not the same thing as a tie, although the concept is closely related. A tie is a particular connection between two particular nodes: for instance, we might say that Node A is tied to Node B. A relation, on the other hand is the sort of action, event or state that creates ties between nodes in a network. For instance, we could say that “friendship” is a relation.
To clarify the difference, here is a sample network in which “friendship” is the relation. There is a tie (an undirected tie) between Al and Betty. Al and Betty are friends. There is also a tie between Betty and Cleo, because Betty and Cleo are friends. There is no tie between Al and Cleo, because Al and Cleo are not friends.
5. On page 37, Hansen et al refer to “multiplexity,” a circumstance in which there are multiple ties based in multiple kinds of relations existing between the same sets of nodes. For instance, the connection between A and B is multiplex when A and B are tennis partners, go out to lunch with each other, live in the same dorm, attend political rallies together and send one another love letters. The opposite of “multiplex” is “simplex.” We would say the connection between Cleo and Doreen is simplex if they only attend the same Introduction to Sociology class but otherwise have no sort of contact with one another.
Prell refers to the idea of multiplexity in an implicit way when she creates a bullet-point list of different kinds of ties on page 7, and indicates that “in some instances, you will find the same individuals popping up as answers time and time again.” Those are multiplex relations.
Exercise #1: The Two Questions that Generate a Social Network
To generate a social network, you need to answer just two questions:
- What kind of node is in your network? That is, what kind of communicator are you studying?
- What kind of tie is in your network? That is, what kind of communication are you studying?
Although there are exceptions (which we’ll discuss later in this course), for purposes of simplicity it is usually best for the social network you create to contain just one kind of communication. If you’re interested in studying two different kinds of communication, it is probably best to create two distinct social networks so that you can clearly compare and contrast them to one another.
Take a moment to consider the variety of different answers you might provide to these two network-generating questions. There are so many ways to answer these questions, which means that there are so many possible networks to create!
It’s your turn to participate. We’re going to use an interactive gizmo called a “Padlet” for you to participate right in the middle of this lecture. Just click (or double-click, depending on the computer you’re using) on the Padlet, and you can type words, upload a picture or a word processing document, even share audio or video. Remember to use your class pseudonym, not your real name, and have fun.
In our first Padlet exercise for this course lecture, I’d like you to provide an example of a social network by answering the two basic questions about networks: What is the node? What is the tie? What could a node be? What could a tie be? Answer these two questions for a hypothetical social network that you imagine. Remember that a node is simply something that can communicate. A tie is simply an observed communication. The participation challenge for this Padlet is for you to be creative and share answers to those questions. To make the challenge fun, you should post an answer that no one has shared in the Padlet yet. Yes, that means the earlier you post the easier the challenge will be!
Exercise #2: Draw Me a Network!
You’ve read about social networks. Now I’d like you to show me a picture of one! Draw me a network graph.
Post a network graph to the “Padlet” wall you see below in whatever way you feel most comfortable. Begin by double-clicking on the padlet to get a post started. Then upload an image file, drag and drop a Microsoft Word file onto the wall, or even take a picture of a hand-drawn network with your webcam. Finally, tell me a bit about your network graph. What are your nodes? What kind of relationship is represented in a tie? Is this an ego-network or some other kind of network? Be sure to sign your work using your class pseudonym so I know the work is yours.
And pssst… don’t be shy: to make this experience really sing, feel free to add notes reacting to others students work.
The Three Different Mainstream Ways to Represent a Network… and Missed Alternatives
Refer to Hansen p. 35 to review the three different ways to represent a network: edge lists (Table 3.2), matrices (Table 3.1) and sociograms (or “network graphs” — Figure 3.2).
Watch this video for a brief consideration of the reasons we think of social networks in these ways and not in others. There are alternative possibilities, but if we believe historical anecdotes, our circles-and-lines approach is due to the morning habits of a mathematician who lived nearly 400 years ago:
Academics have settled not on social boxes, not on social circles, and not on social waves, then, but on social networks — and if in the course of the 20th Century the idea of the “social network” settled in, in the short 21st Century social network analysis has really taken off. Most of you have taken an Introduction to Sociology course, and so you are familiar with the classic sociological paradigms of Conflict Theory, Functionalism and Symbolic Interactionism. If you have taken any upper-level courses in the humanities, you have likely been exposed to its dominant paradigm of Postmodernism. How does “social network analysis” compare as a trend in scholarship? Here are the results of a Google Scholar search of published academic papers containing the phrase “social network analysis,” compared to papers featuring the names of those other paradigms, during the years 2000-2013:
As you can see, at the turn of the 21st Century the relative presence of “social network analysis” showed no remarkable popularity compared to the classic sociological paradigms in academic publications, but for the past six years “social network analysis” has outperformed the three classic sociological paradigmatic phrases, and by an increasingly large margin. In the year 2013, “social network analysis” outperformed “postmodernism” in publications for the first time. You are taking this course at the right time; it looks as though you’re riding the crest of a wave.
One-Mode and Two-Mode Networks
In the last section of her first chapter, Christine Prell plays a bit of a trick, referring to one-mode networks (or “adjacency” networks) and two-mode networks (known when represented with matrices as “incidence matrices,” “event matrices,” or “affiliation matrices“), but not fully explaining them. In case you’re curious, I’ll describe the relationship between one-mode and two-mode networks in different words from Prell’s, then promise you that we’ll return to the subject later. But don’t worry if you feel you don’t understand two-mode networks yet: this is just an introduction, a teaser for later in the semester.
Affiliation is different than communication: it is the act of belonging to a group (Al is a member of the Glee Club), or being a participant in an event (Betty went to the presidential inauguration in 2008), or being a participant in an action (Dave climbed the Eiffel Tower), or having an characteristic (Enid is female).
Affiliation matrices take this social information and try to express it in terms compatible with networks. Let’s consider an example from real life — committee membership by State Senators in the 124th Maine State Legislature of 2011-2012. Let’s start with this membership list:
|Senators on the Agriculture Committee:
|Senators on the Crime Committee:
|Senators on the Labor Committee:
|Senators on the Inland Fisheries Committee:
An affiliation matrix (senators in the rows and committees in columns, written “senators x committees”) puts the lists together. It assigns a zero when a senator is not a member of a committee, and a one when a senator is a member of a committee:
The affiliation matrix above reports new explicit information: it tells us who is NOT on sitting on committees, when the lists really only implicitly reported that information. That information is made explicit when we compare names on one committee list and see if they’re on another committee list too. Let’s turn our powers of comparison to the affiliation matrix, looking at pairs of rows in the matrix to compare senators. For instance, if we compared Senator Bruce Bryant to Senator Troy Jackson, we’d notice that they share one committee membership in common: both are members of the Inland Fisheries Committee. Senator Bruce Bryant and Senator John Nutting also share one committee membership in common: membership on the Agriculture Committee. Senators Gerald Davis and David Trahan, on the other hand, don’t share any committee memberships in common.
We could continue comparing these pairs of senators, writing paragraph after paragraph after paragraph on the subject. Alternatively, we could make an adjacency matrix (senators in rows and senators in columns, written “senators x senators”) to describe that information succinctly. Each cell in the adjacency matrix below contains a number — the number of committees to which two Senators both belong:
Networks aren’t just about people — they can describe connections between committees, too. From the same original affiliation matrix we could describe the members two committees hold in common. The Agriculture and Crime committees hold one member in common — both have John Nutting on them. Could we expect the two committees to act a bit more alike because they have John Nutting on them? Could we consider John Nutting to be a tie between the committees? It’s a distinct possibility: John Nutting is a conduit of information between the two committees, able to inform the Crime committee of the goings on inside Agriculture committee meetings and vice versa. Among these senators, by contrast, there are no members held in common by the Agriculture and Labor committees. They have no such human conduit — no such tie — between them.
As before, we could write paragraph after paragraph considering the ties or lack of ties between all possible pairs of committees. More succinctly, we could present a committees x committees adjacency matrix below:
Pssst… some of you may have noticed an odd set of numbers in the senators x senators and committees x committees matrices. I’ve put those numbers in bold. They’re called the “diagonal” because they form a diagonal line from the upper-left corner to the bottom-right corner of a matrix, and they’re special because — as Prell notes on page 14 — “the diagonal of the matrix represents a sender’s tie with herself.” Prell continues: “The diagonal tends to be ignored in SNA.” But that’s not always true, because the diagonal contains useful information. In the senators x senators matrix, the diagonal indicates how many committee affiliations a senator has (literally, how many committees a senator holds in common with himself or herself). In the committees x committees matrix, the diagonal indicates how many members each committee has. What to do with the diagonal — ignore it, delete it, exploit it — is a recurring question in social network analysis.
This is all nice to know in a particular case, you may be thinking, but what does it tell us generally? In 1974, Ronald Breiger answered that question by arguing that persons and groups have a dualrelation. Breiger uses matrix algebra to lay out his argument, but his argument can be laid out in plain English like this:
- When two people belong to a group (or any other meaningful activity) together, they spend time together. As Scott Feld (1981) points out, this tends to lead to the formation of a social tie.
- As two individuals hold more common group memberships in comon, they will spend more time together. Therefore, the strength of their social tie will increase.
- When two groups hold a member in common, information of various sorts can be more easily communicated from group to group. Common members tie groups to one another.
- As two groups hold more members in common, the strength of the tie between them will increase.
This idea — that people become tied to each other in groups, and that people are the glue holding groups together — is a fundamental premise upon which society is organized. That’s why it’s so important in social network analysis, and we’ll return to this point later in the semester.
Try It For Yourself!
Try taking the following affiliation information from the fictional Edwards High School and converting it into a 2-mode “persons x groups” affiliation matrix, a 1-mode “persons x persons” adjacency matrix, and a 1-mode “groups x groups” adjacency matrix. Look at the information you see below, create your matrices, and check your work by hovering your mouse over the icons that appear after the text “Matrix 1,” “Matrix 2,” and “Matrix 3.” How’d you do?
Don’t Forget Homework
Don’t forget that the syllabus lists homework to be completed each week. As a matter of fact, this week your homework is the syllabus itself! Homework #1 is due by 11:59 pm Eastern time on Sunday, September 13:
- Read the entire course syllabus.
- Read the entire UMA Student Academic Integrity Code.
- Send on any questions or concerns you may have regarding the syllabus and the Student Academic Integrity Code by e-mail to firstname.lastname@example.org; I’ll respond as promptly as possible.
- Complete a quiz about the syllabus and academic integrity code by Sunday September 13 at 11:59 pm. The quiz is listed as “Quiz #1” in the “Homework Assignments” section of our course Blackboard page (look for the “Homework Assignments” link on the left-hand side of our Blackboard page — accessible on the web via http://courses.maine.edu.
Do you have any questions about this lecture or the week’s readings? If so, post them in the comments box below!