Finding and tracking local communities in social networks using differential geometry

Community detection methods in networks can be classified into two domains, global methods and local methods. Many networks are typically very large, making the global community detection methods impractical due to the computational expense. In addition, the constant stream of changes in the structure of networks makes it impossible for anyone to know the structure of the network fully. Therefore, local community detection algorithms, which do not need full knowledge of the structures of the network, have met with renewed interest. This thesis focuses on the problem of finding local communities and tracking them in dynamic networks using derivative-based geometric features by mapping the concepts of derivatives into graph space.