  Convergence guarantees of many resilient consensus algorithms are based on
the graph theoretic properties of $r$- and $(r,s)$-robustness. These algorithms
guarantee consensus of normally behaving agents in the presence of a bounded
number of arbitrarily misbehaving agents if the values of the integers $r$ and
$s$ are sufficiently high. However, determining the largest integer $r$ for
which an arbitrary digraph is $r$-robust is highly nontrivial. This paper
introduces a novel method for calculating this value using mixed integer linear
programming. The method only requires knowledge of the graph Laplacian matrix,
and can be formulated with affine objective and constraints, except for the
integer constraint. Integer programming methods such as branch-and-bound can
allow both lower and upper bounds on $r$ to be iteratively tightened.
Simulations suggest the proposed method demonstrates greater efficiency than
prior algorithms.
