A Graph Theoretic and Mathematical Framework for the Analysis of Linguistic Structures

Abstract

This study proposes a mathematical framework for modelling English linguistic structures using Graph Theory. Various graph models such as Dependency, Tree, Cyclic, Probabilistic, Control Flow, State Transition and Mathematical graphs are used to describe diverse linguistic relationships using selected English Quotes. Mathematical mappings between linguistic elements and graph structures are defined. The study also uses the Principle of Mathematical Induction and the Well Ordering Principle to examine linguistic graph models. Furthermore, the concept of connectivity is explored and appropriate propositions are developed and proven. The proposed framework combines graph theory, discrete mathematics and computational linguistics to provide natural language processing and knowledge representation.