### How central are you?

Thursday, April 23rd, 2009

Since the last two weeks, I contemplate a lot (when I am not Facebook-ing of course) on centrality measures termed in Social Network Analysis (SNA).

Successfully drawing a network of relationship between concepts (or we can simplify them as node), positioning every node in its right locus leads to another task: figuring the form of the network and assessing the importance of every node in the network. Under the wisdom of Graph Theory which elegantly adopted by SNA, importance of nodes an network form are translated as centrality measures. Given to every single network are numbers of every Network Centralization Index; to every nodes in a network are numbers of every Unit Centrality measure. Centralization indices and centrality measures both deal with Degree, Closeness and Betweenness. I skip the formal definitions of the terms, because they just make us confused and they are not so important (for this note). I just jump to the interpretation, my careless interpretation.

I suggest to start this analytical games by drawing any little universe, where every person in the universe is represented by a node. Any universe? Yup! But avoid to pick the universe with you as the central (for example the inner circle of your friend relations) because then it will be trivial. The analysis will give nothing since certainly you are the sun of the universe. Objectively pick a universe, like a scientist does, set the ego outside the research scope. Hmmm… a building where your apartment or your office in or a street where you live, might be a good example. OK, we assume an objective universe finally discovered…

Then, exclusively set the direction of the line apart from the scene, we work on undirected line, simply symmetric relationships. I’m related to you because you are related to me, that is the assumption applied in this scene. If we denote a friendship relation on every line then it means that we do not care about seniority, subordination or other titles degrade the equality status. You are my friend because I am your friend. Draw every possible line between nodes… A sophisticated shape of the relationships map may come in a form of a network….

Now, let’s start exploring the first unit centrality measure, the degree centrality. It deals with how many ingoing and outgoing lines a node holds. Take your node, what is your degree? To what number of person are you befriended? The higher degree you get, the more important you are.

Next, closeness centrality. It is about the shortest path, shortest distance, directedness…. Among all the lines occur in the network, how many is directly connected to you? Count the directly connection…. that is your closeness… The higher closeness you get, the more important you are

Betwenness is about how you connect two nodes in the shortest path. A and B are connected because of you. A scholar denotes betwenness as a measure of the influence a node has over the network… But please do not be swerved by the influential matter… Betweenness actualy (or simply) is about being a bridge… (Bridge over troubled water… the song suddenly rings a bell)

For an illustration, take my experience when on behalf of my friend I asked another friend to do a statistical analysis for her project. A friend who asked the favor said, “I do not know him…, It’s better if you that ask him to do it.” I went to my statistician friend, and the reply came, “OK, I’ll do it.. but it’s only because of you, because you asked me to do, because you are my friend!” In this case, I have a value of betweenness…. Count the bridge you make … that is your betwenness… The higher betwenness you get, the more important you are…

Whew…. so we now have our degree, closeness and betweenness of centrality unit measures…. You know how important are you now….

We now can also figure out how the form of network… Is it dominated by a particular node? The network has a star topology. One node become the central of attention… Or does it seem that everybody shares relatively same value of centrality. If so, we have a circle… We might also have an intermediary, less centralized but not so circular….

Actually the formulae are quite simple, but I do not have capability to compose my own computer program so I turn to Pajek, a software written by Mrvar and Batagelj, experts from University of Ljubljana, Slovenia. The software is nicely named Pajek, which in Slovenian means spider. See the beauty behind this name… Spider… and spider has its net and net becomes network…

Pajek is designed to analysis large network. The software can freely be downloaded from http://vlado.fmf.uni-lj.si/pub/networks/pajek/. Manual and examples also are available. All free!

Hmmm… This note precisely sounds like one of lecture notes….Boring… Certainly!

So, let’s get back to the centrality measures… What are your centrality measures? Are they high? How central are you? How important are you? Are you important? Are you not important?

If you are important, it’s good… it’s great! What else can I say? Congrats!!!! Hip hip hurray!!!!

If you are not important? It’s OK… you are only not important in that objective little universe called office, neighborhood or university. You are not important for not so important person…

But you are important for the most important people, for your closed real friends, for family, for your beloved. “You are the apple of my eye, dear…!” that’s how my father concluded my importance in his sight…

Even better…. you are important in God’s sight… (*)

Wow…

Hmmm… the note turn to be so deviated (as my usual me…)

I better end it right now and continue contemplating…. (also doing my assignment)

(*) Note:

A verse of King David prayer: Keep Me, O Lord, as the apple of *Your eye *