Utilizing graph classes for community detection in social and complex networks

Social network analysis is a cross-disciplinary study of interest to mathematicians, physicists, computer scientists and sociologists. It deals with looking at large networks of interactions and extracting useful or meaningful information from them. One attribute of interest is that of identifying social communities within a network: how such a substructure should be defined is a widely-studied problem in itself. With each new definition, there is a need to study in what applications or context such a definition is appropriate, and develop algorithms and complexity results for the computation of these clusterings. This thesis studies problems related to graph clustering, motivated by the social networking problem of community detection. One main contribution of this thesis is a new definition of a specific kind of family-like community, accompanied by theoretical and computational justifications. Additional results in this thesis include proofs of hardness for the quasi-threshold editing problem and the diameter augmentation problem, as well as improved exact algorithms for cograph and quasi-threshold edge deletion and vertex deletion problems.Graduate Studies, College of (Okanagan)Graduat