This paper presents efficient shared-memory parallel implementations and the first comprehensive experimental study of graph eccentricity estimation algorithms in the literature. The implementations include (1) a simple algorithm based on executing two-pass breadth-first searches from a sample of vertices, (2) algorithms with sub-quadratic worst-case running time for sparse graphs and non-trivial approximation guarantees that execute breadth-first searches from a carefully chosen set of vertices, (3) algorithms based on probabilistic counters, and (4) a well-known 2-approximation algorithm that executes one breadth-first search per connected component. Our experiments on large undirected real-world graphs show that the algorithm based on two-pass breadth-first searches works surprisingly well, outperforming the other algorithms in terms of running time and/or accuracy by up to orders of magnitude.  The high accuracy, efficiency, and parallelism of our best implementation allows the fast generation of eccentricity estimates for large graphs, which are useful in many applications arising in large-scale network analysis.

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