An Introduction to Social Network Analysis
Social network analysis (SNA) is the methodical analysis of social networks. Social network analysis views social relationships in terms of network theory, consisting of nodes (representing individual actors within the network) and ties (which represent relationships between the individuals). These networks are often depicted in a social network diagram, where nodes are represented as points and ties are represented as lines.
Example of a social network diagram Relationships in a network can either be directional or nondirectional. In a directional relationship, one person is the initiator (or source of the relationship) while the other is the receiver (or destination of the relationship). For example, in the diagram above, node 1269 is the source while node 3777 is the destination. Relationships can also be described as dichotomous or valued. A dichotomous relationship is one where the only information that exists is whether or not a relationship exists between two people, where as in a valued relationship, a weight indicating the strength of the relationship is also available. To understand this better, let us look at the following data set from a fictional telecommunications company:
A social diagram representing one of the nodes (3777) in this data set is as follows:
In this diagram, the nodes are marked in dark colors while the weight of the relationship between two nodes are marked in light colors. Since all the relationships in this diagram have weights, all relationships are valued and none of them are dichotomous. Also, all these relationships appear to be directional with a clear source and a clear destination. Two common metrics used to describe social networks are density and degree. Both these metrics represent connectivity but density focuses on the entire network or communities within the network where as degree focuses on the individuals within the network. Network density Density is represents the proportion of possible relationships in a network that are actually present. The value ranges from 0 to 1; the closer the value is to 0, the sparser the network is while the closer the value is to 1, the denser the network is. The number of possible relationships in a network is calculated using the formula:
where n = the number of nodes in the network and 2 is the maximum number of relationships possible between any two nodes in the network. So for example, in a network containing 3 nodes, the maximum number of possible relationships is:
Assuming there are 3 relationships in this network, the density is 3 / 6 or 0.5. Similarly, in a network containing 5 nodes, the maximum number of possible relationships is:
Assuming there are only 4 relationships in this network, the density is 4 / 20 = 0.2. Therefore the first network is denser than the second network (since 0.5 > 0.2). Nodal degree Nodal degree is defined as the total number of relationships involving that node. Degree can be broken into two parts: indegree and outdegree. Indegree is the number of relationships in which a particular node is the target where outdegree is the number of relationships in which a particular node is the source. The following table illustrates nodal degrees in a 7 node relationship:
(Example sourced from SPSS SNA User Guide) In the table above, A’s degree measure is 3 split as indegree = 0 and outdegree = 3.
