involved in the excitation transfer play a fundamental role in the transport, as they make the whole system efficient and robust under perturbations.

Methods
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Tight binding model
-------------------

We analyze the transport properties of discrete systems, comprised by a set of $N$ excitable sites that are modeled as two-level systems. The interactions are described by the tight-binding Hamiltonian

$$H=\sum_{i\neq j}^N \frac{Jr^{3}_{0}}{|\vec r_i-\vec
r_j|^3}\sigma_i^{-}\sigma_j^{+}\ ,
\label{eq:ham}$$

where $J$ is the dimensionless coupling constant and $\sigma_i^{-/+}$ describe the annihilation/creation of an excitation at site $i$. The interaction rate decays cubically with the inter-site distance in accordance with dipole-dipole interaction. Within this model, a *structure* is defined by the positions of the $N$ sites. The initially excited site (input) and the site where the excitation is sought to arrive (output) are located at the diagonally opposite corners of a cube of side $r_0$, while the remaining $N-2$ sites are placed randomly within this cube.

The system is initialized with an excitation on the input site; transport efficiency is defined as the maximal probability to find the excitation at the output site within a short time interval after initialization $$\epsilon=\mathrm{max}_{t\in[0,\mathcal{T}]}|\langle in|\mathrm{e}^{iHt}|out\rangle|^2\ .
\label{eq:emaxtau}$$ The states $| in \rangle$/ $| out \rangle$ denote the 