abstract: Transport properties play a crucial role in several fields of science, as biology, chemistry, sociology, information science, and physics. The behavior of many dynamical processes running over complex networks is known to be closely related to the geometry of the underlying topology that can be described by the spectral properties of such graphs, i.e. the spectrum of the so-called adjacency matrices defining these structures. Here, we generalize this connection to the quantum version of such dynamics processes over large complex networks. In particular, we investigate the relation between static measures of geometrical properties of complex graphs (as shortest path length, graph diameter, etc.) and the (dynamical) capability to quickly and robustly transmit energy (or information) from two distant points, remarkably assisted by external noise and quantum features as coherence, by means of quantum stochastic random walk formalism. Hence, the interplay among geometry, coherence and noise is studied in terms of transport efficiency and relative robustness. These results might pave the way for designing optimal bio-inspired geometries of efficient transport nanostructures that can be used for solar energy and also quantum information and communication technologies.