Network Graph Properties

Business Intelligence class continued the discussion on Network analysis and properties of a network graph. There are many properties of a network that we want to analyze in order to understand the network and compare it with other networks. Structural properties are very important for this analysis.

Degree centrality is the number of links or proportion of links that a particular node has. The degree can be an in degree or an out degree. The degree is usually expressed as a number between 0 and 1. Degree centrality is the number of links that the node has divided by the total number of nodes and subtracting one. Below is an example to calculate this:

Source: http://www.sscnet.ucla.edu/soc/faculty/mcfarland/soc112/cent-ans.htm

Another important feature is the closeness centrality. This describes how close a particular node is to another node based on the shortest path. It basically says how fast you can reach someone when starting at an arbitrary node. Some of the areas it works for is information diffusion or disease transmission. Below is an example of how this is calculated:

Source: http://www.sscnet.ucla.edu/soc/faculty/mcfarland/soc112/cent-ans.htm

Eigenvector Centrality is another important characteristic that we can use to analyze. The Eigenvector centrality takes into account a different measure of importance. If a node is connected to many other nodes, then the node is very important, which is what Google's PageRank uses for webpages. A node does not have importance on its own, but it comes from being connected to other nodes that are connected to other nodes. This is useful because it can tell you how many people can this node reach directly and how well connected the person is.

Gephi will be used throughout this course to visualize the graphs. I was able to use Gephi for the upcoming assignment to analyze my facebook friends to see how everything is interrelated.

Below is my Facebook network built with Gephi and Netvizz app with ranking it by Degree.