***
The real workhorses of SNA are sociograms and sociomatrices. They are essentially two different ways to visualize the exact same data. I like to think of sociograms as the "sexy" way to visualize networks, while sociomatrices are the "useful" way to visualize networks. That is, sociograms are an exciting way to communicate your network analysis to a customer, while sociomatrices are where you're gonna be doing your actual analysis. So let's learn about the interplay between these two visualization modes, shall we?
You saw a simple sociogram last post, and I'll show it again:
Exhibit A1: The Sociogram (Undirected)
Those big blue dots labeled Alice, Bob, and Chuck? Those are called nodes. Nodes represent individual actors, although they need not represent actual individuals. For example, these nodes could just as well represent smaller organizations within one big organization: Tehrik-i-Taliban Pakistan, al Qaeda Central, and al Shabaab. But for illustration sake, let's stick with Alice, Bob, and Chuck.
Those lines with the arrows connecting the nodes? Those are interchangeably referred to as arcs, ties, or links. A link represents a relationship or an action of some kind occurring between two actors. In this case, we say that a link between Alice and Bob means that they "know" one another, but we could just as easily say it means that they "sleep with" one another (I refer the reader to a delightful sexual network analysis of a gonorrhea outbreak). One important nuance here is the presence of arrows. See how the arrows point both ways? That means that the relationship is mutual, or undirected. The action is reciprocated: Alice knows Bob and Bob knows Alice.
When there is only one arrow, we say that the relationship is directed. That is, Bob gave Alice the clap, not the other way around. We would illustrate this as such:
Exhibit A2: The Sociogram (Directed)
I told you this stuff was sexy.
Now let's move on to the unsexy but eminently useful sociomatrix!
Exhibit B1: The Sociomatrix (Undirected)
ALICE | BOB | CHUCK | |
ALICE | 0 | 1 | 0 |
BOB | 1 | 0 | 1 |
CHUCK | 0 | 1 | 0 |
Your eyes are not fooling you: that is a matrix full of 1's and 0's, with the labels of the rows mirroring the labels of the columns. The 1's signify that there is a link between actors while the 0's signify that there is no link between actors. Let's read the matrix from left to right, starting with the row that is labeled Alice. According to the matrix, Alice has no link with Alice (this is not some type of metaphysical statement about Alice's self-loathing: links with oneself make no sense and are registered as 0). She enjoys a link with Bob (1), but no link with Chuck (0). Let's move on to Bob, reading from left to right. He enjoys a link with Alice (1), has no link with himself (0), and has a link with Chuck (1). And so on. The important thing to note is that this matrix articulates the exact same information as the Alice-Bob-Chuck sociogram we saw above.
A sociomatrix of the unfortunate clap scenario mentioned above would look like this:
Exhibit B2: The Sociomatrix (Directed)
ALICE | BOB | |
ALICE | 0 | 0 |
BOB | 1 | 0 |
***
You now understand the most crucial tools for social network analysis. You may be asking yourself why Chad thinks sociomatrices are the "useful" type of visualization. After all, it is hard to look at a matrix of 1's and 0's and glean anything of substance. I agree with you. However, here are a couple painful truths about computer assisted SNA:
Painful Truth 1) SNA programs need to be fed a sociomatrix to provide you with valuable measurements such as degree centrality, betweenness centrality, etc.
Painful Truth 2) SNA programs need to be fed a sociomatrix to spit out a sociogram.
Seriously, are you gonna draw this by hand?
Yeah, I didn't think so.*
*Image ganked from Google, source unknown.
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