  The growth of an interface formed by the hierarchical deposition of particles
of unequal size is studied in the framework of a dynamical network generated by
a horizontal visibility algorithm. For a deterministic model of the deposition
process, the resulting network is scale-free with dominant degree exponent
$\gamma_e = \ln{3}/\ln{2}$ and transient exponent $\gamma_o = 1$. An exact
calculation of the network diameter and clustering coefficient reveals that the
network is scale invariant and inherits the modular hierarchical nature of the
deposition process. For the random process, the network remains scale free,
where the degree exponent asymptotically converges to $\gamma =3$, independent
of the system parameters. This result shows that the model is in the class of
fractional Gaussian noise (fGn) through the relation between the degree
exponent and the series' Hurst exponent $H$. Finally, we show through the
degree-dependent clustering coefficient $C(k)$ that the modularity remains
present in the system.
