Social Network Theory

SNT is the study of social networks. A network is a collection of things that connect. Many things can be seen as a network. A tangled ball of yarn, the road system, your brain and of course people which form a Social Network.

A structural network
Metropolitan Museum of Art. A wonderful network of bambo and ties producing a structure that you can walk on.

A Social Network is not as cut and dry as one would believe by reading popular media and social media. Let’s start with some vocabulary:

Node: The entities in a network (that can act). In a social network these could be people or organizations. In a road network they could be destinations or locations. Consumers and generators in a power distribution network. Math types refer to nodes as vertices.

Tie: Connections between nodes. Also known as edges. These are the paths over which things flow.

Graph: Often used by math types in place of network. That’s why you hear the term Social Graph or Graph Theory in place of Network Theory. Some people talk about nodes, ties and networks and other talk about vertices, edges and graphs.

Simple right? On paper yes. But in a real social application there is more than meets the eye.

Darcy White looks at a piece from Jack the dripper.
A Jackson Pollack painting. The large object which resembles a penguin is Darcy Whyte, author.

Imagine yourself in a pub or restaurant. What is the network? It depends on your definition of a node and of a tie and what you’re trying to accomplish. Most people would see the individuals as nodes (vs. tables, groups, and what have you).

The ties are where it gets exciting.  There are different kinds of ties that we could be interested in. For example “friendship” is a tie. “To know someone” is a tie.  That’s obvious. But there are other ties. What about the handshake network. People are connected if they have shaken hands. It’s clearly different than the friendship network. There are friends that have never shaken hands and people who shake hands that don’t know each other.

At face value this all might seem irrelevant. But if disease propagates the pub, handshakes matter. If support traverses the network friendship matters.

There is also a commerce layer in our imagined pub. The server sells you something. You pay. That’s a connection. Recall that things flow between nodes. Products and money is a flow. You could call this a commerce layer in the network.

Oh no! It’s getting complicated!

Notice that the product only flows in one direction. The wares of the venue go from the service to you and your friends. But generally you don’t give your wares to the venue. This is a directed tie. Flow is in one direction. He/she sold you something but you didn’t sell them anything.

A handshake on the other hand is an undirected tie. Both parties have to do it. Friendship is often similar.

There are other network layers in our pretend venue. The visibility network for example. The who-can-see-who network. This is a very dynamic network (and a directed network by the way). For example from where you sit, you can see some people that can see you and some people that can’t see you. Moments later the network is different. People move. Lighting could change. People drop their glasses. 🙂

With different kinds of ties (or network layers), directed and undirected ties, things start to get very interesting.


It’s interesting to note that directed networks are often more volatile than undirected networks. Imagine a situation where a  bunch of construction workers are doing their business and then someone crosses the street. All the construction workers may find the person crossing the street interesting. So they all pay attention. The person crossing the street can only pay attention to one or a few people. It’s a directed network. It can grow and decay very rapidly. One second nobody is paying attention. The next second a whole crowd. But they aren’t fully reciprocating.

The nodes or actors in the network can link layers together. For example, a server from the commerce layer in the pub (which you don’t know), could link you to a person you should know.

Modeling a social network is usually based on a simplified view of the network. For example Facebook only sees undirected friendship ties. Twitter sees directed ties of attention.

As you can see computer systems can’t model networks well yet. But there are some good examples. Google uses algorithms to look at the ties (or links) between web sites to help assess the quality of sites and pages and the relevance to particular search terms. They use Eigenvector Centrality which is a measure of connectedness of nodes in the network. It’s very useful and explains why their search results are always so relevant compared to other search engines.

Degree: The number of connections that a particular node has. With a directed network we talk about in-degree and out-degree.

Networks also may have randomly formed connections or other patterns in how connections form. Humans often form scale-free networks where some people are very connected and then others are not. With a scale-free network the distribution of ties follows a power law.  The more connected nodes in a network are called Hubs and Authorities.

Scale-free networks are interesting because many natural networks (including social network) follow that pattern. These networks are fairly immune a random removal of ties. There will often be lots of other short routes through the network even when ties are missing. They may be more vulnerable to a focused attack on hubs however.

These networks are called scale-free because if you make the network bigger (adding ties in the same pattern), the  routes between nodes doesn’t increase.

So tell me. What is a social network?

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