A decentralized algorithm for balancing a strongly connected weighted digraph

In this work we propose a decentralized algorithm for balancing a strongly connected weighted digraph. This algorithm relies on the decentralized estimation of the left eigenvector associated to the zero structural eigenvalue of the Laplacian matrix. The estimation is performed through the distributed computation of the powers of the Laplacian matrix itself. This information can be locally used by each agent to modify the weights of its incoming edges so that their sum is equal to the sum of the weights outgoing this agent, i.e., the weighted digraph is balanced. Simulation results are proposed to corroborate the theoretical results.