As we mentioned before, data mining finds a model on data and the mining of social network finds the model on graph data in which the social network is represented.
Social network mining is one application of web data mining; the popular applications are social sciences and bibliometry, PageRank and HITS, shortcomings of the coarse-grained graph model, enhanced models and techniques, evaluation of topic distillation, and measuring and modeling the Web.
When it comes to the discussion of social networks, you will think of Facebook, Google+, LinkedIn, and so on. The essential characteristics of a social network are as follows:
- There is a collection of entities that participate in the network. Typically, these entities are people, but they could be something else entirely.
- There is at least one relationship between the entities of the network. On Facebook, this relationship is called friends. Sometimes, the relationship is all-or-nothing; two people are either friends or they are not. However, in other examples of social networks, the relationship has a degree. This degree could be discrete, for example, friends, family, acquaintances, or none as in Google+. It could be a real number; an example would be the fraction of the average day that two people spend talking to each other.
- There is an assumption of nonrandomness or locality. This condition is the hardest to formalize, but the intuition is that relationships tend to cluster. That is, if entity A is related to both B and C, then there is a higher probability than average that B and C are related.
Here are some varieties of social networks:
- Telephone networks: The nodes in this network are phone numbers and represent individuals
- E-mail networks: The nodes represent e-mail addresses, which represent individuals
- Collaboration networks: The nodes here represent individuals who published research papers; the edge connecting two nodes represent two individuals who published one or more papers jointly
Social networks are modeled as undirected graphs. The entities are the nodes, and an edge connects two nodes if the nodes are related by the relationship that characterizes the network. If there is a degree associated with the relationship, this degree is represented by labeling the edges.
Here is an example in which Coleman's High School Friendship Data from the sna R package is used for analysis. The data is from a research on friendship ties between 73 boys in a high school in one chosen academic year; reported ties for all informants are provided for two time points (fall and spring). The dataset's name is coleman, which is an array type in R language. The node denotes a specific student and the line represents the tie between two students.
