  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 their
variants to achieve resilient consensus. However, determining $r$-robustness is
intractable for large networks. In this paper, we propose a sample-based
algorithm to approximately test $r$-robustness of a digraph with $n$ vertices
and $m$ edges. For a digraph with a moderate assumption on the minimum
in-degree, and an error parameter $0<\epsilon\leq 1$, the proposed algorithm
distinguishes $(r+\epsilon n)$-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 running
time is linear in the number of edges if $\epsilon$ is a constant.
