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Determining the size of a network and its diameter are important functions in distributed systems, as there are a number of algorithms which rely on such parameters, or at least on estimates of those values. The Extrema Propagation technique allows the estimation of the size of a network in a fast, distributed and fault tolerant manner. The technique was previously studied in a simulation setting where rounds advance synchronously and where there is no message loss. This work presents two main contributions. The first, is the study of the Extrema Propagation technique under asynchronous rounds and integrated in the Network Friendly Epidemic Multicast (NeEM) framework. The second, is the evaluation of a diameter estimation technique associated with the Extrema Propagation. This study also presents a small enhancement to the Extrema Propagation in terms of communication cost and points out some other …