Algebraic Connectivity Estimation Based on Decentralized Inverse Power Iteration

In this work, we propose a new scheme to estimate the algebraic connectivity of the graph describing the network topology of a multi-agent system. We consider network topologies modeled by undirected graphs. The main idea is to propose a new decentralized conjugate gradient algorithm and a decentralized compound inverse power iteration scheme. The matrix inversion computation in this scheme is replaced by solving the non-homogeneous linear equations relying on the proposed decentralized conjugate gradient algorithm. With this scheme, we can achieve a fast convergence rate in estimating the algebraic connectivity by setting the parameter μ properly. Simulation results demonstrate the effectiveness of the proposed scheme.