Discrete Distributed Estimation of Algebraic Connectivity and Fiedler Vector

Algebraic connectivity and its associated eigenvector, the Fiedler vector, play a fundamental role in maintaining connectivity in multi-agent systems. However, existing estimation methods often suffer from slow convergence. This letter proposes an efficient discrete distributed algorithm, building on prior work, for estimating algebraic connectivity with exponential convergence. And a corresponding method for approximating the Fiedler vector is also developed, making the approach well-suited for connectivity maintenance tasks. Theoretical analysis establishes the convergence conditions for both algorithms. Numerical simulations on weighted and cycle graphs demonstrate that the proposed approach achieves significantly faster convergence compared to original method.