Toward Maximizing Algebraic Connectivity via Density-Dependent Backbone Construction and Reinforcement Learning Completion

Abstract:This paper studies an open network design problem of constructing graph topologies with maximum algebraic connectivity under fixed numbers of vertices and edges. A density-dependent approach is proposed that decomposes the design task into two stages: a high-quality, low-cost structural backbone construction and a reinforcement learning completion stage. The method selects the backbone based on density, using complete multipartite graphs in dense regimes and Cayley graphs in low-to-intermediate regimes, and then refines the remaining edges through a learning-based procedure. Numerical results show that the proposed method achieves high algebraic connectivity with favorable runtime scalability, outperforming existing methods. These results support a structural-family-first strategy for scalable network design.

Optimization and Control (math.OC); Machine Learning (cs.LG); Combinatorics (math.CO)

arXiv:2610.12697 [math.OC]

(or arXiv:2610.12697v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2610.12697 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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