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The rank of a divisor on a metric graph is a concept appearing in the Riemann-Roch theorem for metric graphs (or tropical curves) due to Gathmann and Kerber, and Mikhalkin and Zharkov. We define a \\emph{rank-determining set} of a metric graph $\\Gamma$ to be a subset $A$ of $\\Gamma$ such that the rank of a divisor $D$ on $\\Gamma$ is always equal to the rank of $D$ restricted on $A$. 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