<p>We study partition problems based on two ostensibly different kinds of energy functionals defined on <i>k</i>-partitions of metric graphs: Cheeger-type functionals whose minimisers are the <i>k</i>-Cheeger cuts of the graph, and the corresponding values are the <i>k</i>-Cheeger constants of the graph; and functionals built using the first eigenvalue of the Laplacian with positive, i.e., absorbing, Robin (delta) vertex conditions at the boundary of the partition elements. We prove existence of minimising <i>k</i>-partitions, <i>k</i> ≥ 2, for both these functionals. We also show that, for each <i>k</i> ≥ 2, as the Robin parameter <i>α</i> → 0, up to a renormalisation the spectral minimal Robin energy converges to the <i>k</i>-Cheeger constant. Moreover, up to a subsequence, the Robin spectral minimal <i>k</i>-partitions converge in a natural sense to a <i>k</i>-Cheeger cut of the graph. Finally, we show that as <i>α</i> → ∞ there is convergence in a similar sense to the corresponding Dirichlet minimal energy and partitions.</p><p>It is strongly expected that similar results hold on general (smooth, bounded) Euclidean domains and manifolds.</p>