The second smallest eigenvalue λ(L) of the Laplacian L of a network G is a parameter that captures important properties of the network. Applications such as synchronization of networked systems, consensus-based algorithms and network connectivity control may require one to regulate the magnitude of λ(L) in order to achieve suitable network performance. The problem of decentralized estimation of λ(L) for directed graphs is thus a relevant problem, yet it has received little attention thus far. We present an algorithm for its estimation and demonstrate its performance.
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