Topological simplification of large-scale knowledge graphs seeks to simplify the structure of knowledge graphs with minimal semantic loss and query time. The paper gives a detailed methodology on reducing the graph, incorporating mathematical equations, evaluation criteria, and analysis of the taxonomy. Graph theoretic operators, such as node contraction and edge pruning along with node motif preservation under constraint optimization are used to formalize the problem. A single set of quality standards are suggested: information retention, connectivity preservation, computational efficiency and downstream task accuracy. The simplification techniques identified in the paper are classified into three paradigms which include structural, heuristic and learning-driven. Graph neural networks and embedding-guided pruning are used in machine learning methods to reduce adaptively using centrality methods, clustering methods, and sparsification methods, unlike heuristic methods that do not use graph neural networks. Experimental results indicate that there are trade-offs between compression ratio and semantics fidelity.