Graph quotients: a topological approach to graphs

This paper develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as relations of cause-effect type. Almost no underlying assumptions are made, other than that the data can be presented in terms of pair-wise relationships between objects/events. This assumption is used to mine for patterns in a dataset defining a reduced graph or a dataset that boils-down or concentrates information into a more compact form. The resulting extracted structure or the set of patterns are manifestly symbolic in nature, as they capture and encode the graph structure of the dataset in terms of a (generative) grammar.