Refined efficient routing with a novel cost function in complex networks

Enhancing information transmission in complex networks is a fundamental problem in network science, particularly in addressing congestion and improving overall efficiency. Traditional shortest path routing strategies tend to overload high-degree nodes, while efficient routing strategies mitigate this issue by minimizing cumulative node degrees along paths. However, such approaches may overly penalize central nodes, leading to suboptimal resource utilization. In this study, we propose a refined efficient routing strategy based on a novel cost function employing a double-logarithmic transformation of node degrees. This design encourages a more balanced use of network resources by appropriately adjusting the cost contribution of both high- and low-degree nodes. The proposed framework integrates topological insights with cost-function optimization, providing both theoretical insights and practical implications for enhanced network design and traffic management. The methodology is validated through extensive simulations, offering theoretical and practical insights into improved network design and traffic distribution.