PREVIOUS ISSUES » Volume 14 Issue 1 January-March 2026

Abstract:

However, optimization in large-scale networks increasingly calls for methods that couple the analytical strength of LP with the structural insight afforded by graph theory. Classic LP models give precise algebraic formulations but mostly fail on scalability and structural interpretability over complex, high-dimensional networks. Inversely, graph-theoretic models capture strong representations of connectivity, flow, and topological relations but lack the needed expressive power to model rich constraints. This study develops a Hybrid LP–Graph Optimization Framework that embeds LP formulations within graph-theoretic structures for improved efficiency, accuracy, and scalability within network-based optimization tasks. Real data is used from the Stanford Large Network Dataset Collection (SNAP). This paper designs a system to transform network structures into adjacency, incidence, and weight matrices in order to represent a unified algebraic–topological scheme. A hybrid solver is developed that embeds LP operations with graph-informed initialization and structural pruning to accelerate computation. Experimental evaluations across various demand-flow scenarios demonstrate that the hybrid model systematically outperforms classical LP and graph-only methods by achieving runtime reductions of 25–35%, faster convergence, and lower memory use. The hybrid method also demonstrates a 15–20% better scalability where, with increased size of the graph, strong performance is maintained and yields solutions of higher stability and lower variance. These results demonstrate that the introduction of graph topology into LP formulations significantly improves their computational behavior and enhances solution quality. A generalizable, robust framework for modern optimization problems that points towards practical applications in routing, resource allocation, communication networks, and large-scale decision systems is given.