Distribution efficiency and structure of complex networks.

Optimized transport networks play a key role in the function of various artificial and natural systems, such as plant or animal vasculature. Part of the function of these flow networks is to efficiently distribute nutrients to the organism. In the case of the animal circulatory system, the oxygen distributed to the tissues is carried by the red blood cells flowing through the capillaries in the blood plasma. The architecture of the network, as defined by its structure and topology controls both the energy dissipated in transferring the viscous fluid (e.g. the blood through the capillaries) and the efficiency of the nutrient transport (e.g. how the oxygen is distributed in the tissue). In this work, we investigate the optimal structure of networks when both energy optimization and transport efficiency are considered. We discuss how the network structure is affected by the trade-offs of different optimization functionals that compete to impose hierarchy and uniformity to the same network.