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This paper aims to explore various network optimization problems using graph theory, focusing on their mathematical formulations and algorithms.

April 18, 2026Open Access

Applications of Graph Theory in Network Optimization: Shortest Path, Spanning Trees, and Flow Problems

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This paper aims to explore various network optimization problems using graph theory, focusing on their mathematical formulations and algorithms.
Detailed formal models for shortest path, spanning tree, and maximum flow problems
Description of Dijkstra’s algorithm, Kruskal’s and Prim’s algorithms, and the Ford-Fulkerson method
Complexity analysis of algorithms with time complexity assessments
Worked numerical examples and experiments on benchmark graphs to validate theoretical predictions
Dijkstra’s algorithm achieves time complexity of O((V + E) log V)
Kruskal’s and Prim’s algorithms both demonstrate O(E log V) complexity
Numerical experiments confirm theoretical complexity predictions for networks ranging from 6 to 500 vertices
Discussions on connections between problem classes through LP duality and matroid theory

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Explores graph theory applications to optimize communication and transportation networks, suggesting further research areas.

Ravikumar J. Awasare (2026) studied this question.

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