Coexistence of loop and tree structures in transport networks

Transport networks are pervasive in nature, often as a result of some optimization processes. A number of theories explain networks exhibiting either loops or tree configurations. On the contrary, an explanation of the coexistence of tree and loop structures remains a challenge unless flow unsteadiness or channel redundancy is introduced. We propose a framework based on a modified channel construction cost, providing coexistence also in steady-state conditions. Extensive simulations support the robustness of our approach. The presence of loops allows flow distribution to approach the theoretical scaling exponent -1/2, a result so far not obtained in the single source configuration.