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One of the intensely studied concepts of network robustness is$r$-robustness, which is a network topology property quantified by an integer$r$. It is required by mean subsequence reduced (MSR) algorithms and theirvariants to achieve resilient consensus. However, determining $r$-robustness isintractable for large networks. In this paper, we propose a sample-basedalgorithm to approximately test $r$-robustness of a digraph with $n$ verticesand $m$ edges. For a digraph with a moderate assumption on the minimumin-degree, and an error parameter $0<\epsilon\leq 1$, the proposed algorithmdistinguishes $(r+\epsilon n)$-robust graphs from graphs which are not$r$-robust with probability $(1-\delta)$. Our algorithm runs in$\exp(O((\ln{\frac{1}{\epsilon\delta}})/\epsilon^2))\cdot m$ time. The runningtime is linear in the number of edges if $\epsilon$ is a constant.

A Sample-Based Algorithm for Approximately Testing $r$-Robustness of a Digraph