An Infinity Norm-Based Pseudo-Decentralized Discrete-Time Algorithm for Computing Algebraic Connectivity

In some applications of multiagent networks, it is desired that each agent can evaluate how well the network is connected. In this paper, we propose a novel discrete-time algorithm for each agent to compute the algebraic connectivity of the network in a pseudo-decentralized manner. The proposed algorithm requires less computational cost than the conventional algorithm. We also analyze the dynamical behavior of the proposed algorithm and prove under some assumptions on the parameter values and the initial state values of the agents that all agents can compute the algebraic connectivity.