Optimal linear labelings and eigenvalues of graphs
Discrete Applied Mathematics
Laplace eigenvalues of graphs—a survey
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method
SIAM Journal on Scientific Computing
A Graph Based Method for Generating the Fiedler Vector of Irregular Problems
Proceedings of the 11 IPPS/SPDP'99 Workshops Held in Conjunction with the 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing
A decentralized algorithm for spectral analysis
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A scheme for robust distributed sensor fusion based on average consensus
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Foundations and Trends® in Networking
Probabilistic Estimation of Network Size and Diameter
LADC '09 Proceedings of the 2009 Fourth Latin-American Symposium on Dependable Computing
On quantized consensus by means of gossip algorithm: part ii: convergence time
ACC'09 Proceedings of the 2009 conference on American Control Conference
Diffusion LMS strategies for distributed estimation
IEEE Transactions on Signal Processing
Performance analysis of the consensus-based distributed LMS algorithm
EURASIP Journal on Advances in Signal Processing
Hearing the clusters of a graph: A distributed algorithm
Automatica (Journal of IFAC)
Local clustering of large graphs by approximate fiedler vectors
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Computer Science Review
Consensus-Based Distributed Total Least Squares Estimation in Ad Hoc Wireless Sensor Networks
IEEE Transactions on Signal Processing
Diffusion Bias-Compensated RLS Estimation Over Adaptive Networks
IEEE Transactions on Signal Processing
Matrix Analysis
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The Fiedler vector of a graph is the eigenvector corresponding to the smallest non-trivial eigenvalue of the graph's Laplacian matrix. The entries of the Fiedler vector are known to provide a powerful heuristic for topology inference, e.g., to identify densely connected node clusters, to search for bottleneck links in the information dissemination, or to increase the overall connectivity of the network. In this paper, we consider ad hoc networks where the nodes can process and exchange data in a synchronous fashion, and we propose a distributed algorithm for in-network estimation of the Fiedler vector and the algebraic connectivity of the corresponding network graph. The algorithm is fully scalable with respect to the network size in terms of per-node computational complexity and data transmission. Simulation results demonstrate the performance of the algorithm.