Minimal implications base for social network analysis

Currently, social network (SN) analysis is focused on the discovery of activity and social relationship patterns. Usually, these relationships are not easily and completely observed. Therefore, it is relevant to discover substructures and potential behavior patterns in SN. Recently, formal concept analysis (FCA) has been applied for this purpose. FCA is a concept analysis theory that identifies concept structures within a data set. The representation of SN patterns through implication rules based on FCA enables the identification of relevant substructures that cannot be easily identified. The authors’ approach considers a minimum and irreducible set of implication rules (stem base) to represent the complete set of data (activity in the network). Applying this to an SN is of interest because it can represent all the relationships using a reduced form. So, the purpose of this paper is to represent social networks through the steam base.

The authors’ approach permits to analyze two-mode networks by transforming access activities of SN into a formal context. From this context, it can be extracted to a minimal set of implications applying the NextClosure algorithm, which is based on the closed sets theory that provides to extract a complete, minimal and non-redundant set of implications. Based on the minimal set, the authors analyzed the relationships between premises and their respective conclusions to find basic user behaviors.

The experiments pointed out that implications, represented as a complex network, enable the identification and visualization of minimal substructures, which could not be found in two-mode network representation. The results also indicated that relations among premises and conclusions represent navigation behavior of SN functionalities. This approach enables to analyze the following behaviors: conservative, transitive, main functionalities and access time. The results also demonstrated that the relations between premises and conclusions represented the navigation behavior based on the functionalities of SN. The authors applied their approach for an SN for a relationship to explore the minimal access patterns of navigation.

The authors present an FCA-based approach to obtain the minimal set of implications capable of representing the minimum structure of the users’ behavior in an SN. The paper defines and analyzes three types of rules that form the sets of implications. These types of rules define substructures of the network, the capacity of generation users’ behaviors, transitive behavior and conservative capacity when the temporal aspect is considered.