Consensus-based Distributed Estimation of Laplacian Eigenvalues of Undirected Graphs

International audienceIn this paper, we present a novel algorithm for estimating eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system or a wireless sensor network. As recently shown, the average consensus matrix can be written as a product of Laplacian based consensus matrices whose stepsizes are given by the inverse of the nonzero Laplacian eigenvalues. Therefore, by solving the factorization of the average consensus matrix, we can infer the Laplacian eigenvalues. We show how solving such a matrix factorization problem in a distributed way. In particular, we formulate the problem as a constrained consensus problem. The proposed algorithm does not require great resources in both computation and storage. This algorithm can also be viewed as a way for decentralizing the design of finite-time average consensus protocol recently proposed in the literature. Eventually, the performance of the proposed algorithm is evaluated by means of simulation results

Consensus-based Distributed Estimation of Laplacian Eigenvalues of Undirected Graphs

International audienceIn this paper, we present a novel algorithm for estimating eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system or a wireless sensor network. As recently shown, the average consensus matrix can be written as a product of Laplacian based consensus matrices whose stepsizes are given by the inverse of the nonzero Laplacian eigenvalues. Therefore, by solving the factorization of the average consensus matrix, we can infer the Laplacian eigenvalues. We show how solving such a matrix factorization problem in a distributed way. In particular, we formulate the problem as a constrained consensus problem. The proposed algorithm does not require great resources in both computation and storage. This algorithm can also be viewed as a way for decentralizing the design of finite-time average consensus protocol recently proposed in the literature. Eventually, the performance of the proposed algorithm is evaluated by means of simulation results

Collaborative Network Monitoring by Means of Laplacian Spectrum Estimation and Average Consensus

International audienceThis paper concerns collaborative monitoring of the robustness of networks partitioned into subnetworks.We consider the critical threshold of a network and the effective graph resistance (Kirchhoff index)of a sub-graph characterizing the interconnection of sub-networks, that are partitioned from the given network asrobustness metric. In which, the critical threshold depends only on the two first moments of the degree distributionwhile the Kirchhoff index can be computed with Laplacian eigenvalues. Therefore, we show how to estimate jointlythe Laplacian eigenvalues and the two first moments of the degree distribution in a distributed way