Sharing on Social Network Analysis

What is Social Network Analysis (SNA) ?

Social Network Analysis (SNA) is the study of social relations among a set of actors. For instance, people, groups, organizations, computers, URLs, and other connected information/knowledge entities. The nodes in the network are the people and groups while the links show relationships or flows between the nodes. SNA provides both a visual and a mathematical analysis of human relationships. We can base on the analysis and conduct new form of information and knowledge.

My knowledge on SNA

    Figure 1: Social Network
The above figures shows a simple social network, In Social Network Analysis (SNA), it can be represented by adjacency matrix or sociomatrix like the following:

The symbol, "1", represent the link exists between two nodes while represents there is no relationships between them This kind of social network is an undirected graph.

Let L be the number of links in a network, and g is the number of nodes.

In this case, L = 6 and g = 5
In order to find out the most influential people within the social network. We take the above example, several techniques can be used. 

1. Density 

It measures the closeness of a network, is an indicator for the general level of connectedness of the graph
The value of computed density is between 0 and 1.
Density = (L/ [g(g-1) / 2]) = 2* 6/20  = 0.6
2. Centrality

Three standard centrality measures capture a wide range of “importance” in a network:

2.1 Degree Centrality

It counts the number of direct connections a node has:
For the below graph, each value in "Values" rows means the Degree of the node i, we denote it as D(node i)
For the Normialized/ Standardized value,  D(node i) / (g-1)

Result:

Network Centralization = 66.67%


2.2 Closeness Centrality

Closeness represents the mean of the geodesic distances between some particular node and all other nodes connected with in. It describes the average distances between one node and all other nodes connected with it.

The formula is like the following:

Result:

Network Centralization (Closeness) = 58.33%

2.3 Betweenness Centrality

It is a measure of the potential for control as an actor who is high in “betweenness” is able to act as a gatekeeper controlling the flow of resources (information, money, power, e.g.) between the alters that he or she connects.

It can be calculated by the following formula:

Result:

Network Centralization (Betweenness) = 56.25%

In figure 1, we can find out David is the most influential people within the social network.

Conclusion
Centrality is a basic technique to measure how central an individual is positioned in a social network.

For the closeness centrality basically counting the inverse of the average shortest-path distance from the vertex to any other vertex in the graph. It can be viewed as the efficiency of each individual in spreading information to all others.

Actually, beside of the above techniques, if we transform the internet web-pages into a complicated directed graph , we can also use ranking algorithm, for example: PageRank, Hits, EigenRumor, etc They are the methods to find out the rankings. Good homepage will have a good ranking.

As SNA become more and more popular, those SNA technique will help us make the social network data to be high conceptional level into new information and knowledge in different aspects. We can find out and understand more behavior of each social network user and develop a better semantic web in the future. 

On the other hand, we need more sampling in order to make the analysis to be more accurate. However, it may lack of sufficient computing resources to handle large sampling datasets.