Single genus geometric maximal graph filtering and data analysis applications

It is a very current method to model complex systems with different levels of heterogeneity with networks and to analyze data on the system by applying various network analysis techniques. This thesis deals with the analysis of this type of system by geometrically embedded in a manifold and filtering it. A filtering method is presented involving r-clicks of the network that models the complex system based on the genus of a manifold. By geometrically and topologically filtering the correlation networks in dense relationships, it is possible to deduce the maximal relationships by losing the network's minimal information. Similar to the methods available in the literature, this new filtering method that we have presented works for single genus manifold embedding. This ensures that the underlying geometry of the network is also taken into account. This method, which will be applied to three different types of data groups, is expected to be used in multidisciplinary studies and to form a basis for data analysis techniques belonging to different disciplines.